Question

match each expression to the factored form of the expression.
$49x^{2}+4$
a. $(7x + 2)^{2}$
$49x^{2}-4$
b. prime
$49x^{2}+28x + 4$
c. $(7x - 2)^{2}$
$49x^{2}-28x + 4$
d. $(7x + 2)(7x - 2)$
question help: video ebook

Explanation:

Step1: Analyze $49x^2 + 4$

This is a sum of squares: $(7x)^2 + 2^2$. Sum of squares cannot be factored over real numbers, so it is prime.

Step2: Analyze $49x^2 - 4$

This is a difference of squares: $(7x)^2 - 2^2$. Use difference of squares formula $a^2-b^2=(a+b)(a-b)$.
$\text{Factored form}=(7x+2)(7x-2)$

Step3: Analyze $49x^2 + 28x + 4$

This is a perfect square trinomial: $(7x)^2 + 2(7x)(2) + 2^2$. Use perfect square formula $a^2+2ab+b^2=(a+b)^2$.
$\text{Factored form}=(7x+2)^2$

Step4: Analyze $49x^2 - 28x + 4$

This is a perfect square trinomial: $(7x)^2 - 2(7x)(2) + 2^2$. Use perfect square formula $a^2-2ab+b^2=(a-b)^2$.
$\text{Factored form}=(7x-2)^2$

Answer:

$49x^2 + 4$ → b. prime
$49x^2 - 4$ → d. $(7x + 2)(7x - 2)$
$49x^2 + 28x + 4$ → a. $(7x + 2)^2$
$49x^2 - 28x + 4$ → c. $(7x - 2)^2$