Question

What is the factored form of the expression?

4x2 – 81y2
A. (2x + 9)(2x – 9)
B. (2x + 9y)(2x – 9y)
C. (2x + 9y)2
D. (2x – 9y)2

Factor the polynomial.
54c3d4 + 9c4d2
A. 9c3d2(d2 + 6c)
B. 9c3d2(6d2 +
c.
C. 9c4d2(d2 + 6)
D. 9c4d2(6d2 + 1)

Answer 1

4x^2 – 81y^2
= (2x)^2- (9y)^2
= (2x+ 9y)(2x -9y)
Choose B. (2x + 9y)(2x – 9y)

54c^3d^4 + 9c^4d^2
= 9c^3d^2(6d^2+ c)
Choose B. 9c^3d^2(6d^2+ c)

Answer 2

(1) The correct option is, (B)
`(2x+9y)(2x-9y)`

(2) The correct option is, (B)
`9c^3d^2(6d^2+c)`

Explanation :

• Solution for part (1) :

As we know that a polynomial is a mathematical expression of more that two algebraic terms, the sum of several terms which contains different powers of same variables.

The given expression is,

`4x^2-81y^2`

Breaks into simpler terms, we get:

`\Rightarrow (2x)^2-(9y)^2`

Now applying
`a^2-b^2=(a+b)(a-b)` identity, we get:

`\Rightarrow (2x+9y)(2x-9y)`

Therefore, the factored form of the expression is,
`(2x+9y)(2x-9y)`

• Solution for part (2) :

The given expression is,

`54c^3d^4+9c^4d^2`

Now taking common things, we get:

`9c^3d^2(6d^2+c)`

Therefore, the factor of polynomial is,
`9c^3d^2(6d^2+c)`