Simplify (5x^3+4x^2+6x-3)+(-2x^3+3x^2-7x+9)-(5x+3)(4x^2+x-1)

$(5 x^{3} + 4 x^{2} + 6 x - 3) + (- 2 x^{3} + 3 x^{2} - 7 x + 9) - (5 x + 3) (4 x^{2} + x - 1)$

Step 1

Remove parentheses.

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - (5 x + 3) (4 x^{2} + x - 1)$

Step 2

Simplify each term.

Apply the distributive property.

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 + (- (5 x) - 1 \cdot 3) (4 x^{2} + x - 1)$

Multiply $5$ by $- 1$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 + (- 5 x - 1 \cdot 3) (4 x^{2} + x - 1)$

Multiply $- 1$ by $3$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 + (- 5 x - 3) (4 x^{2} + x - 1)$

Expand $(- 5 x - 3) (4 x^{2} + x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 5 x (4 x^{2}) - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 5 \cdot 4 x \cdot x^{2} - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 5 \cdot 4 (x^{2} x) - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 5 \cdot 4 (x^{2} x^{1}) - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 5 \cdot 4 x^{2 + 1} - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Add $2$ and $1$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 5 \cdot 4 x^{3} - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Multiply $- 5$ by $4$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 5 x \cdot x - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

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

Move $x$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 5 (x \cdot x) - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Multiply $x$ by $x$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 5 x^{2} - 5 x \cdot - 1 - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Multiply $- 1$ by $- 5$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 5 x^{2} + 5 x - 3 (4 x^{2}) - 3 x - 3 \cdot - 1$

Multiply $4$ by $- 3$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 5 x^{2} + 5 x - 12 x^{2} - 3 x - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 5 x^{2} + 5 x - 12 x^{2} - 3 x + 3$

Subtract $12 x^{2}$ from $- 5 x^{2}$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 5 x - 3 x + 3$

Subtract $3 x$ from $5 x$ .

$5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 2 x + 3$

Step 3

Simplify by adding terms.

Combine the opposite terms in $5 x^{3} + 4 x^{2} + 6 x - 3 - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 2 x + 3$ .

Add $- 3$ and $3$ .

$5 x^{3} + 4 x^{2} + 6 x - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 2 x + 0$

Add $5 x^{3} + 4 x^{2} + 6 x - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 2 x$ and $0$ .

$5 x^{3} + 4 x^{2} + 6 x - 2 x^{3} + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 2 x$

Subtract $2 x^{3}$ from $5 x^{3}$ .

$3 x^{3} + 4 x^{2} + 6 x + 3 x^{2} - 7 x + 9 - 20 x^{3} - 17 x^{2} + 2 x$

Subtract $20 x^{3}$ from $3 x^{3}$ .

$- 17 x^{3} + 4 x^{2} + 6 x + 3 x^{2} - 7 x + 9 - 17 x^{2} + 2 x$

Add $4 x^{2}$ and $3 x^{2}$ .

$- 17 x^{3} + 7 x^{2} + 6 x - 7 x + 9 - 17 x^{2} + 2 x$

Subtract $17 x^{2}$ from $7 x^{2}$ .

$- 17 x^{3} - 10 x^{2} + 6 x - 7 x + 9 + 2 x$

Subtract $7 x$ from $6 x$ .

$- 17 x^{3} - 10 x^{2} - x + 9 + 2 x$

Add $- x$ and $2 x$ .

$- 17 x^{3} - 10 x^{2} + x + 9$

Simplify (5x^3+4x^2+6x-3)+(-2x^3+3x^2-7x+9)-(5x+3)(4x^2+x-1)

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