Question

What values are needed to make each expression a perfect square trinomial? x2 2x x2 – 20x x2 5x.

Answer 1

The expression as a perfect square trinomial is $\rm x^2+4x+4$.

The expression as a perfect square trinomial is $\rm x^2-20x+100$

The expression as a perfect square trinomial is $\rm x^2+4x+\dfrac{25}{4}$.

Given that

The given equations are as follows;

$\rm x^2 + 2x + \\\\ x^2 -20x +\\\\ x^2 + 5x +$

We have to determine

What values are needed to make each expression a perfect square trinomial?

According to the question

To know more about the values are needed to make a perfect square trinomial following all the steps given below.

A perfect square trinomial is equal to;

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

1. The given equation is,

$\rm x^2 + 2x +$

Then,

Compare with the formula of a perfect square trinomial.

$\rm x^2+2ax+a^2= x^2+4x\\ \\ 4x=2ax\\ \\ a = \dfrac{4x}{2x}\\ \\ a=2$

Substitute the value of a

$\rm x^2+2ax+a^2= x^2+4x+(2)^2\\ \\ x^2+2ax+a^2= x^2+4x+4$

The expression as a perfect square trinomial is $\rm x^2+4x+4$.

2. The given equation is,

$\rm x^2 - 20x +$

Then,

Compare with the formula of a perfect square trinomial.

$\rm x^2+2ax+a^2= x^2-20x\\ \\ -20x=2ax\\ \\ a = \dfrac{-20x}{2x}\\ \\ a=-10$

Substitute the value of a

$\rm x^2+2ax+a^2= x^2 -20x+(-10)^2\\ \\ x^2+2ax+a^2= x^2-20x+100$

The expression as a perfect square trinomial is $\rm x^2-20x+100$.

3. The given equation is,

$\rm x^2 + 5x +$

Then,

Compare with the formula of a perfect square trinomial.

$\rm x^2+2ax+a^2= x^2+5x\\ \\ 5x=2ax\\ \\ a = \dfrac{5x}{2x}\\ \\ a=\dfrac{5}{2}$

Substitute the value of a

$\rm x^2+2ax+a^2= x^2+4x+(\dfrac{5}{2})^2\\ \\ x^2+2ax+a^2= x^2+4x+\dfrac{25}{4}$

The expression as a perfect square trinomial is $\rm x^2+4x+\dfrac{25}{4}$.

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