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Exercise

$\left(ax+b\right)^2=a^2x^2+2abx+b^2$

Step-by-step Solution

1

The trinomial $a^2x^2+2abx+b^2$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$
2

Using the perfect square trinomial formula

$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{a^2x^2}\:and\:b=\sqrt{b^2}$
3

Factoring the perfect square trinomial

$\left(ax+b\right)^2=\left(ax+b\right)^{2}$
4

If the bases are the same, then the exponents must be equal to each other

$2=2$
5

$2$ equals to $2$

true

Final answer to the exercise

true

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Main Topic: Exponential Equations

Exponential equations are those where the unknown appears only in the exponents of powers of constant bases.

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