Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 21

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Question 1
1 / -0

Find the product $$(a^2 + b)(a + b^2)$$

A
$$a^3 + b^3 + 2ab(ab-1)$$

B
$$a^2 + b^2 +2ab-3b^2$$

C
$$a^2 + b^2 + ab(ab+b^2)$$

D
$$a^3 + b^3 + ab(ab+1)$$

Solution

$$(a^2 + b)(a + b^2)$$
$$=a^2(a + b^2)+b(a + b^2)$$
$$=a^3+a^2b^2+ab+b^3$$
$$=a^3+b^3+ab(ab+1)$$
Question 2
1 / -0

Simplify: $$x(3x+2)$$

A
$$3x^2+2$$

B
$$3x+2$$

C
$$3x^2+2x$$

D
$$3x^2+x$$

Solution

$$x(3x+2)=3x^2+2$$
$$L.H.S=x(3x+2)$$
$$=3x^2+2x \neq R.H.S$$
The correct statement is $$x(3x+2)=3x^2+2x$$
Question 3
1 / -0

The value of $$(x^2y)(2x)(3y^3)$$ is

A
$$12x^2y^4$$

B
$$6x^3y^4$$

C
$$3x^3y^4$$

D
$$x^3y^4$$

Solution

$$(x^2y)(2x)(3y^3)$$
First: $$(2)(3) = 6$$
Then: $$(x^3)(y^4)$$
So, $$(x^2y)(2x)(3y^3)= 6x^3y^4$$
Question 4
1 / -0

What is the product of $$(2a+5b)$$ and $$(a-3b)$$?

A
$$2a^2-2ab-15b^2$$

B
$$2a^2-ab-15b^2$$

C
$$2a^2+2ab-15b^2$$

D
$$2a^2+11ab-15b^2$$

Solution

The product of $$(2a+5b)(a-3b)$$$$=2a(a-3b)+5b(a-3b)$$
$$ =2a^2-6ab+5ab-15b^2$$
$$=2a^2-ab-15b^2$$
Question 5
1 / -0

$$(a + b)^2-(a -b)^2$$ will be equal to $$2ab$$:

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

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

$$=a^2+2ab+b^2-a^2+2ab-b^2$$

$$=4ab$$.

Hence, answer is $$4ab$$ but not $$2ab$$.

Option $$B$$ is correct.
Question 6
1 / -0

To multiply two binomials, we multiply each term of one .......... and add the products.

A
Bionomlal by each term of the other

B
Only the variable part

C
Only the constant part

D
None of these

Solution

To multiply two binomials, we multiply each term of one binomial by each term of the other and add the products.
for e.g:-
$$(x+3)(x+8)=x^2+8x+3x+24$$
$$=x^2+11x+24$$
Question 7
1 / -0

Find the solution of $$(2x+6)^2$$.

A
$$x^2+24x+36$$

B
$$4x^2+24x+6$$

C
$$4x^2+24x+36$$

D
$$4x^2-24x+36$$

Solution

$$(2x+6)^2 = (2x+6)(2x+6)$$
= $$2x.2x+2x.6+6.2x+6.6$$
= $$4x^2+12x+12x+36$$
= $$4x^2+24x+36$$
Question 8
1 / -0

What is the coefficient of $$x$$ when $$-x + 6$$ is multiplied by $$2x - 3$$?

A
$$-15$$

B
$$15$$

C
$$-9$$

D
$$9$$

Solution

We have, $$(-x+6)(2x-3) $$
$$=-x(2x-3)+6(2x-3)$$
$$=-2x^2+3x+12x-18 $$
$$= -2x^2+15x-18$$
Hence, coefficient of $$x$$ is $$15$$.
Question 9
1 / -0

The coefficient of the product of two monomials is not equal to the product of their coefficient.

A
True

B
False

C
Sometimes

D
Data insufficient

Solution

The given statement is not true. We take an example.

$$2x, 3y$$ are two monomials with coefficients $$2$$ and $$3$$ respectively.
Now, $$(2x)(3y)=6xy$$, it is also monomial with coefficient $$6,$$ which is a product of $$2$$ and $$3.$$

Hence, option $$B$$ is correct.
Question 10
1 / -0

$$(a + b)^{2} = (a + b)\times$$ ____

A
$$ab$$

B
$$2ab$$

C
$$(a + b)$$

D
$$(a - b)$$

Solution

We know that $$x^{2}=x\times x$$
Then $$(a+b)^{2}=(a+b)\times (a+b)$$

Hence, the answer is (C)

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Algebraic Expressions and Identities Test - 21

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Algebraic Expressions and Identities Test - 21

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Question 1

$$a^3 + b^3 + 2ab(ab-1)$$

$$a^2 + b^2 +2ab-3b^2$$

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

$$a^3 + b^3 + ab(ab+1)$$

Solution

Question 2

$$3x^2+2$$

$$3x+2$$

$$3x^2+2x$$

$$3x^2+x$$

Solution

Question 3

$$12x^2y^4$$

$$6x^3y^4$$

$$3x^3y^4$$

$$x^3y^4$$

Solution

Question 4

$$2a^2-2ab-15b^2$$

$$2a^2-ab-15b^2$$

$$2a^2+2ab-15b^2$$

$$2a^2+11ab-15b^2$$

Solution

Question 5

True

False

Ambiguous

Data insufficient

Solution

Question 6

Bionomlal by each term of the other

Only the variable part

Only the constant part

None of these

Solution

Question 7

$$x^2+24x+36$$

$$4x^2+24x+6$$

$$4x^2+24x+36$$

$$4x^2-24x+36$$

Solution

Question 8

$$-15$$

$$15$$

$$-9$$

$$9$$

Solution

Question 9

True

False

Sometimes

Data insufficient

Solution

Question 10

$$ab$$

$$2ab$$

$$(a + b)$$

$$(a - b)$$

Solution

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