Question

Which Trinomials are perfect square trinomials?

Answer 1

Trinomials that are perfect square trinomials are (C)  $16z^{4}+48z^{2}+36$ and (D) $9m^{2}+36m+36$.

$(a+b)^{2}=a^{2}+2ab+b^{2}$

We will check every trinomials in given options.

(A) $25a^{2}-40a+64$

     $25a^{2} = (5a)^{2}$

     $64 = 8^{2}$

     $-40a \neq 2(5a)(8)$

     Hence, its not a perfect square.

(B) $x^{2}-6x-16$

     $x^{2} = (x)^{2}$

     $-16 \neq 4^{2}$

     $-6x \neq 2(x)(4)$

     Hence, its not a perfect square.

(C) $16z^{4}+48z^{2} +36$

     $16z^{4} = (4z^{2} )^{2}$

     $36 = 6^{2}$

     $48z^{2}=2(4z^{2} )(6)$

    $16z^{4}+48z^{2} +36 = (4z^{2}+6 )^{2}$

     Hence, its a perfect square.

(D) $9m^{2}+36m+36$

     $9m^{2} = (3m)^{2}$

     $36 = 6^{2}$

     $36m=2(3m)(6)$

    $9m^{2}+36m+36 = (3m+6)^{2}$

     Hence, its a perfect square.

Therefore, only (C) and (D) are perfect square.

To learn more about trinomials here:

brainly.com/question/8985142

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