Simplify (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1)

$(5 x^{2} + 13 x - 4) - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)$

Step 1

Simplify each term.

Apply the distributive property.

$5 x^{2} + 13 x - 4 - (17 x^{2}) - (7 x) - - 19 + (5 x - 7) (3 x + 1)$

Simplify.

Multiply $17$ by $- 1$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - (7 x) - - 19 + (5 x - 7) (3 x + 1)$

Multiply $7$ by $- 1$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x - - 19 + (5 x - 7) (3 x + 1)$

Multiply $- 1$ by $- 19$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + (5 x - 7) (3 x + 1)$

Expand $(5 x - 7) (3 x + 1)$ using the FOIL Method.

Apply the distributive property.

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 5 x (3 x + 1) - 7 (3 x + 1)$

Apply the distributive property.

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 5 x (3 x) + 5 x \cdot 1 - 7 (3 x + 1)$

Apply the distributive property.

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 5 x (3 x) + 5 x \cdot 1 - 7 (3 x) - 7 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 5 \cdot 3 x \cdot x + 5 x \cdot 1 - 7 (3 x) - 7 \cdot 1$

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

Move $x$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 5 \cdot 3 (x \cdot x) + 5 x \cdot 1 - 7 (3 x) - 7 \cdot 1$

Multiply $x$ by $x$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 5 \cdot 3 x^{2} + 5 x \cdot 1 - 7 (3 x) - 7 \cdot 1$

Multiply $5$ by $3$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} + 5 x \cdot 1 - 7 (3 x) - 7 \cdot 1$

Multiply $5$ by $1$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} + 5 x - 7 (3 x) - 7 \cdot 1$

Multiply $3$ by $- 7$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} + 5 x - 21 x - 7 \cdot 1$

Multiply $- 7$ by $1$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} + 5 x - 21 x - 7$

Subtract $21 x$ from $5 x$ .

$5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} - 16 x - 7$

Step 2

Simplify by adding terms.

Subtract $17 x^{2}$ from $5 x^{2}$ .

$- 12 x^{2} + 13 x - 4 - 7 x + 19 + 15 x^{2} - 16 x - 7$

Add $- 12 x^{2}$ and $15 x^{2}$ .

$3 x^{2} + 13 x - 4 - 7 x + 19 - 16 x - 7$

Subtract $7 x$ from $13 x$ .

$3 x^{2} + 6 x - 4 + 19 - 16 x - 7$

Subtract $16 x$ from $6 x$ .

$3 x^{2} - 10 x - 4 + 19 - 7$

Simplify by adding and subtracting.

Add $- 4$ and $19$ .

$3 x^{2} - 10 x + 15 - 7$

Subtract $7$ from $15$ .

$3 x^{2} - 10 x + 8$

Simplify (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1)

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