Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Multiply:
$$ 8ab^2 $$ by $$-4a^3b^4 $$ .

A
$$-32a^4b^7 $$

B
$$-32a^4b^6 $$

C
$$-32a^4b^5 $$

D
$$-32a^5b^6 $$

Solution

$$8ab^2\times (-4a^3b^4)$$
$$=8\times (-4)a^{1+3}b^{2+4}$$
$$=-32a^4b^6$$
Question 2
1 / -0

Multiply: $$ab, a b$$

A
$$a^2b$$

B
$$a^2b^2$$

C
$$ab^3$$

D
$$a^3b^3$$

Solution

$$ab\times a b$$
$$={ a }^{ 1+1 }\times{ b }^{ 1+1 }$$
$$={ a }^{ 2 }{ b }^{ 2 }$$
Question 3
1 / -0

Multiply: $$a + b, 7a^2b^2$$

A
$$a^3b^6 + a^2b^3$$

B
$$7a^3b^2 + 7a^2b^3$$

C
$$7a^5b^2 + 3a^2b^3$$

D
$$a^3b^2 + 7a3b^3$$

Solution

$$a + b, 7a^2b^2$$
$$=(a + b)\times (7a^2b^2)$$
$$=7a^3b^2+7a^2b^3$$
Question 4
1 / -0

Multiply : $$(a^2 + b)$$ and $$ (a + b^2)$$

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

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

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

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

Solution

$$(a^2 + b) (a + b^2)$$
$$=a^2(a+b^2)+b(a+b^2)$$
$$=a^3+a^2b^2+ab+b^3$$
Question 5
1 / -0

Multiply $$(2x + 5)$$ and $$(4x-3)$$.

A
$$4x^2 + 14x-15$$

B
$$4x^2 + 14x+15$$

C
$$8x^2 + 14x-15$$

D
$$8x^2 + 14x+15$$

Solution

$$(2x+5)\times (4x-3)$$
$$=2x(4x-3)+5(4x-3)$$
$$=8x^2-6x+20x-15$$
$$=8x^2+14x-15$$
Question 6
1 / -0

Simplify: $$5x(2x+3y)$$

A
$$10x^2+15xy$$

B
$$10x^4+15y$$

C
$$10y^2+5xy$$

D
$$10x^2+15x$$

Solution

$$5x(2x+3y)$$
$$=10x^2+15xy$$
Question 7
1 / -0

Find the product of $$x ,x^2, x^3 ,x^4$$

A
$$x^{11}$$

B
$$x^{8}$$

C
$$x^{9}$$

D
$$x^{10}$$

Solution

The exponent or product rule states that while multiplying two powers having the same base, we have to add the exponents.

$$\Rightarrow x\times x^2\times x^3\times x^4$$

$$\Rightarrow x^{1+2+3+4}$$

$$\Rightarrow x^{10}$$
Question 8
1 / -0

The product of $$4x^2 - 7x + 19$$ and $$(- 2x)$$ when $$x= 0$$ is:

A
$$19$$

B
$$-38$$

C
$$17$$

D
$$0$$

Solution

Any real number when multiplied by 0 gives 0.
Here at $$x=0$$, $$-2x = 0$$ and hence the result of multiplication will also be zero.
Question 9
1 / -0

Simplify: $$5{ x }^{ 2 }(x+5)+25$$

A
$$\\ 5{ x }^{ 3 }+25{ x }+25$$

B
$$5{ x }^{ 3 }+50x$$

C
$$5{ x }^{ 3 }+25{ x }^{ 2 }+25$$

D
$$5{ x }^{ 3 }+25x$$

Solution

$$5{ x }^{ 2 }(x+5)+25\\ =5{ x }^{ 3 }+25{ x }^{ 2 }+25$$
Question 10
1 / -0

Multiply: $$a^2 -9, 4a$$

A
$$4a^3 - 36a$$

B
$$3a^3 - 36a$$

C
$$3a^3 +36a$$

D
$$4a^3 + 36a$$

Solution

$$a^2- 9, 4a$$
$$=a^2- 9\times 4a$$
$$=4a^3-36a$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 18

Result

Algebraic Expressions and Identities Test - 18

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SHARING IS CARING

Question 1

$$-32a^4b^7 $$

$$-32a^4b^6 $$

$$-32a^4b^5 $$

$$-32a^5b^6 $$

Solution

Question 2

$$a^2b$$

$$a^2b^2$$

$$ab^3$$

$$a^3b^3$$

Solution

Question 3

$$a^3b^6 + a^2b^3$$

$$7a^3b^2 + 7a^2b^3$$

$$7a^5b^2 + 3a^2b^3$$

$$a^3b^2 + 7a3b^3$$

Solution

Question 4

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

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

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

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

Solution

Question 5

$$4x^2 + 14x-15$$

$$4x^2 + 14x+15$$

$$8x^2 + 14x-15$$

$$8x^2 + 14x+15$$

Solution

Question 6

$$10x^2+15xy$$

$$10x^4+15y$$

$$10y^2+5xy$$

$$10x^2+15x$$

Solution

Question 7

$$x^{11}$$

$$x^{8}$$

$$x^{9}$$

$$x^{10}$$

Solution

Question 8

$$19$$

$$-38$$

$$17$$

$$0$$

Solution

Question 9

$$\\ 5{ x }^{ 3 }+25{ x }+25$$

$$5{ x }^{ 3 }+50x$$

$$5{ x }^{ 3 }+25{ x }^{ 2 }+25$$

$$5{ x }^{ 3 }+25x$$

Solution

Question 10

$$4a^3 - 36a$$

$$3a^3 - 36a$$

$$3a^3 +36a$$

$$4a^3 + 36a$$

Solution

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