Simplify (3x+3)^2+(x+5)(x-4)

${(3 x + 3)}^{2} + (x + 5) (x - 4)$

Step 1

Simplify each term.

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

$(3 x + 3) (3 x + 3) + (x + 5) (x - 4)$

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

Apply the distributive property.

$3 x (3 x + 3) + 3 (3 x + 3) + (x + 5) (x - 4)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 3 + 3 (3 x + 3) + (x + 5) (x - 4)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Multiply $3$ by $3$ .

$9 x^{2} + 9 x + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Multiply $3$ by $3$ .

$9 x^{2} + 9 x + 9 x + 3 \cdot 3 + (x + 5) (x - 4)$

Multiply $3$ by $3$ .

$9 x^{2} + 9 x + 9 x + 9 + (x + 5) (x - 4)$

Add $9 x$ and $9 x$ .

$9 x^{2} + 18 x + 9 + (x + 5) (x - 4)$

Expand $(x + 5) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$9 x^{2} + 18 x + 9 + x (x - 4) + 5 (x - 4)$

Apply the distributive property.

$9 x^{2} + 18 x + 9 + x \cdot x + x \cdot - 4 + 5 (x - 4)$

Apply the distributive property.

$9 x^{2} + 18 x + 9 + x \cdot x + x \cdot - 4 + 5 x + 5 \cdot - 4$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$9 x^{2} + 18 x + 9 + x^{2} + x \cdot - 4 + 5 x + 5 \cdot - 4$

Move $- 4$ to the left of $x$ .

$9 x^{2} + 18 x + 9 + x^{2} - 4 \cdot x + 5 x + 5 \cdot - 4$

Multiply $5$ by $- 4$ .

$9 x^{2} + 18 x + 9 + x^{2} - 4 x + 5 x - 20$

Add $- 4 x$ and $5 x$ .

$9 x^{2} + 18 x + 9 + x^{2} + x - 20$

Step 2

Simplify by adding terms.

Add $9 x^{2}$ and $x^{2}$ .

$10 x^{2} + 18 x + 9 + x - 20$

Add $18 x$ and $x$ .

$10 x^{2} + 19 x + 9 - 20$

Subtract $20$ from $9$ .

$10 x^{2} + 19 x - 11$

Simplify (3x+3)^2+(x+5)(x-4)

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