Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

What is the product of $$(x-2x)^2$$?

A
$$2x^2$$

B
$$x-2x^2$$

C
$$x^2$$

D
$$8x^2$$

Solution

$$(x-2x)^2 = (x-2x)(x-2x)$$
$$=$$ $$x.x-x.2x-2x.x+2x.2x$$
$$=$$ $$x^2-2x^2-2x^2+4x^2$$
$$=x^2$$
Question 2
1 / -0

Evaluate: $$-3z^2(-4x^2+10z^4-4xz^5)$$

A
$$12x^2z^2-30z^6+12z^10$$

B
$$12x^2z^2-30z^8+12z^10$$

C
$$12x^4-30z^6+12z^7$$

D
$$12x^2z^2-30z^6+12xz^7$$

Solution

$$-3z^2(-4x^2+10z^4-4xz^5)$$
Multiply each term of the parenthesis by the monomial keeping the addition or subtraction sign same.
$$=$$ $$-3z^2.(-4x^2)+-3z^2.10z^4-(-3z^2).4xz^5$$
$$=$$ $$12x^2z^2-30z^6+12xz^7$$
Question 3
1 / -0

Find the value of $$(2x+5)(2x-5)$$.

A
$$4x-25$$

B
$$4x^2-25$$

C
$$2x^2-25$$

D
$$4x^2-5$$

Solution

We know that binomial identities for $$(x+y)(x-y)=x^2-y^2$$
$$\therefore (2x+5)(2x-5) = (2x)^2-5^2$$
$$=$$ $$4x^2-25$$
Question 4
1 / -0

Multiply: $$6x^5(-3x^4-2x^3+x^2)$$

A
$$-18x^9-12x^8+6x^7$$

B
$$-18x^5-12x^8+6x^7$$

C
$$-18x^9-12x^5+6x^7$$

D
$$-18x^9-12x^8+7x^7$$

Solution

$$6x^5(-3x^4-2x^3+x^2)$$
Multiply each term of the parenthesis by the monomial keeping the addition or subtraction sign same.
$$=$$ $$6x^5.-3x^4-6x^5.2x^3+6x^5.x^2$$
$$=$$ $$-18x^9-12x^8+6x^7$$
Question 5
1 / -0

Simplify the following expression: $$(s-r)^2-(s+r)^2$$

A
$$2sr$$

B
$$2s^2+2r^2$$

C
$$-4sr$$

D
$$2s^2-2r^2$$

Solution

We know that binomial identities for $$(x+y)^2=x^2+2xy+y^2$$
and $$(x-y)^2=x^2-2xy+y^2$$
So, $$(s-r)^2-(s+r)^2$$ $$=$$ $$s^2-2sr+r^2-s^2-2sr-r^2$$
$$=$$ $$-4sr$$
Question 6
1 / -0

The value of $$-3x(5k^2+y)$$ is

A
$$-9k^2x-3xy$$

B
$$-15k^2x-3xy$$

C
$$-15k^3x-3xy$$

D
$$-5k^2x-3xy$$

Solution

We need to find value of $$-3x(5k^2+y)$$
Multiply $$-3x$$ to the inside bracket, we get
=$$-15k^2x-3xy$$
Question 7
1 / -0

Multiply: $$4x^2z(3x^2y^2-4xz)$$

A
$$2x^4y^2z-16x^3z^2$$

B
$$12x^4y^2z-16x^3z^2$$

C
$$12x^4yz-16x^3z^2$$

D
$$12x^4y^2z-16x^2z^2$$

Solution

$$4x^2z(3x^2y^2-4xz)$$
Multiply each term of the parenthesis by the monomial keeping the addition or subtraction sign same.
= $$4x^2z.3x^2y^2-4x^2z.4xz$$
= $$12x^4y^2z-16x^3z^2$$
Question 8
1 / -0

Simplify: $$7a^3(-4a^4+6a^5)$$

A
$$14a^7$$

B
$$14a^8$$

C
$$-28a^7+42a^8$$

D
$$-28a^7+42a^{15}$$

Solution

$$7a^3(-4a^4+6a^5)$$
Multiply each term of the parenthesis by the monomial keeping the addition or subtraction sign same.
$$=$$ $$7a^3.-4a^4+7a^3.6a^5$$
$$=$$ $$-28a^7+42a^8$$
Question 9
1 / -0

Reduce the following expression using binomial identities: $$(3x+5)(3x+10)$$.

A
$$9x^2+45x+50$$

B
$$9x^2-45x+50$$

C
$$9x^2+45x-50$$

D
$$9x^2+45-50$$

Solution

We know that binomial identities for $$(x+y)(x+z)=x^2+(y+z)x+yz$$
So, $$x = 3x, y = 5, z = 10$$
$$=$$ $$(3x)^2+(5+10)3x+5\times 10$$
$$=$$ $$9x^2+45x+50$$
Question 10
1 / -0

If $$x\Box y=(x+y)^2-(x-y)^2$$. Then $$\sqrt 4\Box \sqrt 5=$$.

A
$$0$$

B
$$8\sqrt5$$

C
$$10\sqrt5$$

D
$$15$$

E
$$20$$

Solution

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 36

Result

Algebraic Expressions and Identities Test - 36

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SHARING IS CARING

Question 1

$$2x^2$$

$$x-2x^2$$

$$x^2$$

$$8x^2$$

Solution

Question 2

$$12x^2z^2-30z^6+12z^10$$

$$12x^2z^2-30z^8+12z^10$$

$$12x^4-30z^6+12z^7$$

$$12x^2z^2-30z^6+12xz^7$$

Solution

Question 3

$$4x-25$$

$$4x^2-25$$

$$2x^2-25$$

$$4x^2-5$$

Solution

Question 4

$$-18x^9-12x^8+6x^7$$

$$-18x^5-12x^8+6x^7$$

$$-18x^9-12x^5+6x^7$$

$$-18x^9-12x^8+7x^7$$

Solution

Question 5

$$2sr$$

$$2s^2+2r^2$$

$$-4sr$$

$$2s^2-2r^2$$

Solution

Question 6

$$-9k^2x-3xy$$

$$-15k^2x-3xy$$

$$-15k^3x-3xy$$

$$-5k^2x-3xy$$

Solution

Question 7

$$2x^4y^2z-16x^3z^2$$

$$12x^4y^2z-16x^3z^2$$

$$12x^4yz-16x^3z^2$$

$$12x^4y^2z-16x^2z^2$$

Solution

Question 8

$$14a^7$$

$$14a^8$$

$$-28a^7+42a^8$$

$$-28a^7+42a^{15}$$

Solution

Question 9

$$9x^2+45x+50$$

$$9x^2-45x+50$$

$$9x^2+45x-50$$

$$9x^2+45-50$$

Solution

Question 10

$$0$$

$$8\sqrt5$$

$$10\sqrt5$$

$$15$$

$$20$$

Solution

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