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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

A9c3d2(d2 + 6c)
B9c3d2(6d2 +
C
C9c4d2(d2 + 6)
D9c4d2(6d2 + 1)

Verified Answer :

Billymkhoi

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 :

(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, \(9c^3d^2(6d^2+c)\)

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