Are these practice questions for We Distribute, Yet Things Multiply based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 8 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for We Distribute, Yet Things Multiply free?

Yes. Every chapter includes free practice questions for Class 8 students to get you started.

What types of questions are included?

The practice set for We Distribute, Yet Things Multiply mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for We Distribute, Yet Things Multiply for full coverage.

How many practice questions are there for We Distribute, Yet Things Multiply?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

We Distribute, Yet Things Multiply Class 8 Mathematics Practice Questions with Answers

easy

Explain the steps to expand the product

(p+q)(r+s)

using the distributive property.

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easy

Recall and write the identity for the product of a sum and difference,

(a+b)(a-b)

.

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easy

List the three main algebraic identities for the square of a sum, the square of a difference, and the product of a sum and difference. For each identity, explain what the variables 'a' and 'b' represent and write the expanded form.

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easy

Critique the following simplification and justify your reasoning: A student simplifies

(3x - 5y)^2

to

9x^2 - 25y^2

.

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easy

Examine the following pattern made of squares. Analyze the pattern and write an algebraic expression for the number of squares in the

n^{th}

figure.

Figure 1: 1 square Figure 2: 4 squares (a 2x2 grid) Figure 3: 9 squares (a 3x3 grid)

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easy

State the distributive property of multiplication over addition for any three numbers

a, b,

and

c

.

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easy

Apply the distributive property to expand the expression

(2a - 5)(3b + 4)

.

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easy

Propose a quick method to compute

97^2

using the identity

(a-b)^2

and justify why it is efficient.

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easy

Apply the identity for the square of a sum to calculate

(205)^2

.

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easy

A student was asked to find the product of

(x-5)(x+2)

and gave the answer

x^2 - 10

. Critique the student's answer, explain the error by referring to the distributive property, and provide the correct result.

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easy

Describe the process of simplifying the expression

5x^2 + 3y - 2x^2 + 7y

.

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easy

Write the algebraic identity for

(a-b)^2

.

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easy

Write the algebraic identity for

(a+b)^2

.

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easy

Compare the values of

(4m + 3n)^2

and

(4m - 3n)^2

when

m=2

and

n=1

. Which expression yields a larger result? Show your calculations.

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easy

Calculate the value of

104 \times 96

using a suitable algebraic identity.

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medium

Explain what is meant by an 'algebraic identity' and provide an example.

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medium

Describe how to use the identity

(a+b)^2 = a^2 + 2ab + b^2

to find the value of

103^2

.

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medium

Justify why the expressions

(p-q)^2

and

(q-p)^2

are equivalent. Propose two different methods for your justification.

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medium

Justify, using an algebraic proof, that the difference between the squares of any two consecutive integers is equal to the sum of those two integers.

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medium

Define the term 'like terms' in algebra.

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medium

A student claims that for any two positive numbers

x

and

y

, the expression

(x+y)^2

is always greater than

x^2 + y^2

. Evaluate this claim and provide a justification for your conclusion using an algebraic identity.

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medium

Explain how to use the identity

(a+b)(a-b) = a^2 - b^2

to mentally calculate the product

31 \times 29

.

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medium

Without performing direct multiplication, calculate the value of

105 \times 107

using an appropriate identity.

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medium

Evaluate the statement: 'The product of two consecutive even numbers is always 1 less than the square of the odd number between them.' Justify your conclusion with an algebraic proof.

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medium

If

a + b = 9

and

ab = 20

, analyze the relationship to find the value of

a^2 + b^2

.

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medium

Simplify the algebraic expression:

(3p + 2q)^2 - (3p - 2q)^2

.

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medium

Propose a method to mentally calculate the product of two numbers that are equidistant from a round number (like 50 or 100), for example,

48 \times 52

. Justify your method using an algebraic identity.

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medium

Create an expression of the form

(x+a)(x-b)

such that its expansion is

x^2 + 3x - 10

. Justify your choice of

a

and

b

.

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medium

Analyze the statement:

(3x+5)^2 = 9x^2 + 25

. Is this correct? Justify your answer by showing the correct expansion.

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medium

The length of a rectangular field is

(5x + 4)

meters and its breadth is

(5x - 4)

meters. Calculate the area of the field as an algebraic expression. Then, if

x = 10

, find the numerical value of the area.

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medium

List the four terms obtained when you expand

(3x+2)(y+7)

before combining any like terms.

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medium

Create a trinomial that is a perfect square and whose terms involve two variables,

m

and

n

, and has a constant coefficient of 16 for the

m^2

term.

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medium

Apply the distributive property to find the product of

(x-5)

and

(x^2 + 2x + 3)

and simplify the result.

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medium

Summarize the geometric interpretation of the identity

(a+b)^2 = a^2 + 2ab + b^2

. Describe the shapes and their areas.

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medium

A square lawn has a side length of

x

meters. A concrete path of uniform width

2

meters is built all around the inside of the lawn. Analyze the situation to find an algebraic expression for the area of the path. Then, calculate the area of the path if the lawn has a side length of

30

meters.

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medium

Expand the expression

(4x - \frac{1}{3}y)^2

using an appropriate identity.

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hard

Analyze the following statement and demonstrate its validity using algebra: "If you take any two consecutive odd numbers, their product increased by 1 is always a perfect square of an even number."

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hard

Identify the property of multiplication used in the following step:

(x+5)(x+2) = (x+5)x + (x+5)2

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hard

Describe a general method for multiplying any two binomials of the form

(ax+b)

and

(cx+d)

. Explain each step and how to simplify the final expression.

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hard

Formulate a general identity for

(a+b+c)^2

. Use the distributive property twice to derive your formula. First, treat

(a+b)

as a single term.

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hard

Create a word problem involving the area of a walkway around a rectangular pool where the solution requires the use of the identity

a^2 - b^2 = (a+b)(a-b)

for simplification. Formulate the algebraic expression and solve it for specific values.

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hard

From a rectangular sheet of paper with dimensions

(3x+5)

cm by

(2x+4)

cm, a square of side

(x-1)

cm is removed. Analyze this to find an expression for the area of the remaining sheet. Calculate the remaining area if

x=5

cm.

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hard

Formulate an algebraic expression for the area of the shaded region in the figure below. The figure consists of a large square of side 'a' with a smaller square of side 'b' removed from one corner, and two rectangles of sides 'a' by 'b' attached as shown. Justify that this area is equivalent to

(a+b)(a-b)

.

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hard

If

x + \frac{1}{x} = 5

, evaluate the value of

x^2 + \frac{1}{x^2}

without solving for

x

. Justify the steps in your method.

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hard

Create a binomial of the form

(ax+b)

which, when multiplied by

(2x-3)

, results in a product where the coefficient of the

x

term is zero.

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We Distribute, Yet Things MultiplyClass 8 Mathematics Practice Questions