Simplify (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7)

$(4 x^{2} + 8 x + 15) + (x^{2} - x - 27) - (x + 5) (x - 7)$

Remove parentheses.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - (x + 5) (x - 7)$

Simplify each term.

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 + (- x - 1 \cdot 5) (x - 7)$

Multiply $- 1$ by $5$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 + (- x - 5) (x - 7)$

Expand $(- x - 5) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x (x - 7) - 5 (x - 7)$

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x \cdot x - x \cdot - 7 - 5 (x - 7)$

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x \cdot x - x \cdot - 7 - 5 x - 5 \cdot - 7$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - (x \cdot x) - x \cdot - 7 - 5 x - 5 \cdot - 7$

Multiply $x$ by $x$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} - x \cdot - 7 - 5 x - 5 \cdot - 7$

Multiply $- 7$ by $- 1$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 7 x - 5 x - 5 \cdot - 7$

Multiply $- 5$ by $- 7$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 7 x - 5 x + 35$

Subtract $5 x$ from $7 x$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 2 x + 35$

Simplify by adding terms.

Combine the opposite terms in $4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 2 x + 35$ .

Subtract $x^{2}$ from $x^{2}$ .

$4 x^{2} + 8 x + 15 - x - 27 + 0 + 2 x + 35$

Add $4 x^{2} + 8 x + 15 - x - 27$ and $0$ .

$4 x^{2} + 8 x + 15 - x - 27 + 2 x + 35$

Subtract $x$ from $8 x$ .

$4 x^{2} + 7 x + 15 - 27 + 2 x + 35$

Add $7 x$ and $2 x$ .

$4 x^{2} + 9 x + 15 - 27 + 35$

Simplify by adding and subtracting.

Subtract $27$ from $15$ .

$4 x^{2} + 9 x - 12 + 35$

Add $- 12$ and $35$ .

$4 x^{2} + 9 x + 23$