Question

What values are needed to make each expression a perfect square trinomial?
x2 + 4x +_____________
x2 – 10x + ____________

Answer 1

Answer:

Part a) $x^{2}+4x+4$

Part b) $x^{2}-10x+25$

Step-by-step explanation:

we know that

A perfect square trinomial is equal to

$(x+a)^{2} =x^{2}+2ax+a^{2}$

Part a) we have

$x^{2}+4x$

Compare with the formula of a perfect square trinomial

$x^{2}+4x=x^{2}+2ax+a^{2}$

so

$4x=2ax$

$4=2a$

$a=2$

therefore

$(x+a)^{2} =(x+2)^{2}=x^{2}+4x+4$

Part b) we have

$x^{2}-10x$

Compare with the formula of a perfect square trinomial

$x^{2}-10x=x^{2}+2ax+a^{2}$

so

$-10x=2ax$

$-10=2a$

$a=-5$

therefore

$(x+a)^{2} =(x-5)^{2}=x^{2}-10x+25$

Answer 2

The values are needed to make each expression a perfect square trinomial x^2 + 4x + 4 and x^2 – 10x + 25.

What is a perfect square?

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

A. $x^{2} +4x+4$

A perfect square trinomial is

$(x+a)^2 = x^2 + 2ax + a^2$

Compare with the formula of a perfect square trinomial

4x = 2ax

4 = 2a

a = 2

Therefore, $(x+a)^2 = (x+2)^2 = x^{2} +4x+4$

B. $x^{2} -10x + 25$

A perfect square trinomial is

$(x+a)^2 = x^2 + 2ax + a^2$

Compare with the formula of a perfect square trinomial

-10x = 2ax

-10 = 2a

a = -5

Therefore, $(x+a)^2 = (x-5)^2 = x^{2} -10x+25$.

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