Checkpoint: Polynomial Identities Solution

Determine if a polynomial identity exists. Explain.

${(4 x)}^{2} + 24 x + 9 = {(4 x + 3)}^{2}$

16 x^{2} + 24 x + 9

(4 x + 3) (4 x + 3) 16 x^{2} + 12 x + 12 x + 9 16 x^{2} + 24 x + 9

This is an identity because both sides of the equation are equal.

Note

If you are able to multiply and simplify the right side of the equation using mental math, remember to write down the expression.

Q: How can you determine if you have an identity?
A: Simplify each side to determine if they are equal.

Q: What value or values will make an identity true?
A: Any value will make an identity true.