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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
A. 9c3d2(d2 + 6c)
B. 9c3d2(6d2 +
c.
C. 9c4d2(d2 + 6)
D. 9c4d2(6d2 + 1)

Respuesta :

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) [tex](2x+9y)(2x-9y)[/tex]

(2) The correct option is, (B) [tex]9c^3d^2(6d^2+c)[/tex]

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,

[tex]4x^2-81y^2[/tex]

Breaks into simpler terms, we get:

[tex]\Rightarrow (2x)^2-(9y)^2[/tex]

Now applying [tex]a^2-b^2=(a+b)(a-b)[/tex] identity, we get:

[tex]\Rightarrow (2x+9y)(2x-9y)[/tex]

Therefore, the factored form of the expression is, [tex](2x+9y)(2x-9y)[/tex]

  • Solution for part (2) :

The given expression is,

[tex]54c^3d^4+9c^4d^2[/tex]

Now taking common things, we get:

[tex]9c^3d^2(6d^2+c)[/tex]

Therefore, the factor of polynomial is, [tex]9c^3d^2(6d^2+c)[/tex]