Find the Perfect Square Trinomial 9x^2-24x+16

$9 x^{2} - 24 x + 16$

Factor out the $9$

$9 (x^{2} - \frac{8 x}{3} + \frac{16}{9})$

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

Multiply the numerator by the reciprocal of the denominator.

${(- (\frac{8}{3} \cdot \frac{1}{2}))}^{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

${(- (\frac{2 (4)}{3} \cdot \frac{1}{2}))}^{2}$

Cancel the common factor.

${(- (\frac{2 \cdot 4}{3} \cdot \frac{1}{2}))}^{2}$

Rewrite the expression.

${(- \frac{4}{3})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{4}{3}$ .

${(- 1)}^{2} {(\frac{4}{3})}^{2}$

Apply the product rule to $\frac{4}{3}$ .

${(- 1)}^{2} \frac{4^{2}}{3^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{4^{2}}{3^{2}}$

Multiply $\frac{4^{2}}{3^{2}}$ by $1$ .

$\frac{4^{2}}{3^{2}}$

Raise $4$ to the power of $2$ .

$\frac{16}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{16}{9}$

Add $\frac{16}{9}$ to get the perfect square trinomial.

$9 (x^{2} - \frac{8 x}{3} + \frac{16}{9} + \frac{16}{9})$

Simplify.

Combine fractions.

Combine the numerators over the common denominator.

$9 (x^{2} + \frac{- 8 x}{3} + \frac{16 + 16}{9})$

Add $16$ and $16$ .

$9 (x^{2} + \frac{- 8 x}{3} + \frac{32}{9})$

Move the negative in front of the fraction.

$9 (x^{2} - \frac{8 x}{3} + \frac{32}{9})$

Apply the distributive property.

$9 x^{2} + 9 (- \frac{8 x}{3}) + 9 (\frac{32}{9})$

Simplify.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{8 x}{3}$ into the numerator.

$9 x^{2} + 9 \frac{- 8 x}{3} + 9 (\frac{32}{9})$

Factor $3$ out of $9$ .

$9 x^{2} + 3 (3) \frac{- 8 x}{3} + 9 (\frac{32}{9})$

Cancel the common factor.

$9 x^{2} + 3 \cdot 3 \frac{- 8 x}{3} + 9 (\frac{32}{9})$

Rewrite the expression.

$9 x^{2} + 3 (- 8 x) + 9 (\frac{32}{9})$

Multiply $- 8$ by $3$ .

$9 x^{2} - 24 x + 9 (\frac{32}{9})$

Cancel the common factor of $9$ .

Cancel the common factor.

$9 x^{2} - 24 x + 9 (\frac{32}{9})$

Rewrite the expression.

$9 x^{2} - 24 x + 32$

Find the Perfect Square Trinomial 9x^2-24x+16

Related Questions

Support LCMGCF.com by disabling your adblocker.