Simplify x^2-7x+12+(x-3)^2 ?

$x^{2} - 7 x + 12 + {(x - 3)}^{2}$ ?

Step 1

Simplify each term.

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$x^{2} - 7 x + 12 + (x - 3) (x - 3)$

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$x^{2} - 7 x + 12 + x (x - 3) - 3 (x - 3)$

Apply the distributive property.

$x^{2} - 7 x + 12 + x \cdot x + x \cdot - 3 - 3 (x - 3)$

Apply the distributive property.

$x^{2} - 7 x + 12 + x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - 7 x + 12 + x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3$

Move $- 3$ to the left of $x$ .

$x^{2} - 7 x + 12 + x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$x^{2} - 7 x + 12 + x^{2} - 3 x - 3 x + 9$

Subtract $3 x$ from $- 3 x$ .

$x^{2} - 7 x + 12 + x^{2} - 6 x + 9$

Step 2

Simplify by adding terms.

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} - 7 x + 12 - 6 x + 9$

Subtract $6 x$ from $- 7 x$ .

$2 x^{2} - 13 x + 12 + 9$

Add $12$ and $9$ .

$2 x^{2} - 13 x + 21$