Louise Completed The Work Shown Below., (5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9, Determine If Louise2019s Answer Is Correct. Explain.

Louise completed the work shown below.

(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise's answer is correct. Explain.

 

Answer:

(5x³ + 3)²  = 25x⁶ + 30x³ + 9

The product of a square of binomial is a perfect square trinomial.

Louises answer "25x⁶ + 9" is not correct.

Step-by-step explanation:

(5x³ + 3)²  ⇒  a square of binomial

= (5x³ + 3)(5x³ + 3)

= 25x⁶ + 15x³ + 15x³ + 9

= 25x⁶ + 30x³ + 9

Louises answer is NOT correct because she only multiplied the first terms and last terms, hence her answer "25x⁶ + 9".

In solving for the product of the square of binomial, this is the pattern:

(a) Square the first term  ⇒ (5x³) (5x³) = 25x⁶

(b) Twice the product of (first term) and (last term)  ⇒ 2 (5x³)(3) = 30x³

(c) Square the last term ⇒  (30(3) = 9

Combine the results ⇒ 25x⁶ + 30x³ + 9 ⇒  a perfect square trinomial

The product of a square of binomial is a perfect square trinomial.


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