Write in Standard Form (3x-2)(-x^2-10x-7)

$(3 x - 2) (- x^{2} - 10 x - 7)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(3 x - 2) (- x^{2} - 10 x - 7)$ by multiplying each term in the first expression by each term in the second expression.

$3 x (- x^{2}) + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot - 1 x \cdot x^{2} + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

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

Move $x^{2}$ .

$3 \cdot - 1 (x^{2} x) + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

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

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

$3 \cdot - 1 (x^{2} x^{1}) + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

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

$3 \cdot - 1 x^{2 + 1} + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Add $2$ and $1$ .

$3 \cdot - 1 x^{3} + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Multiply $3$ by $- 1$ .

$- 3 x^{3} + 3 x (- 10 x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Rewrite using the commutative property of multiplication.

$- 3 x^{3} + 3 \cdot - 10 x \cdot x + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

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

Move $x$ .

$- 3 x^{3} + 3 \cdot - 10 (x \cdot x) + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Multiply $x$ by $x$ .

$- 3 x^{3} + 3 \cdot - 10 x^{2} + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Multiply $3$ by $- 10$ .

$- 3 x^{3} - 30 x^{2} + 3 x \cdot - 7 - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Multiply $- 7$ by $3$ .

$- 3 x^{3} - 30 x^{2} - 21 x - 2 (- x^{2}) - 2 (- 10 x) - 2 \cdot - 7$

Multiply $- 1$ by $- 2$ .

$- 3 x^{3} - 30 x^{2} - 21 x + 2 x^{2} - 2 (- 10 x) - 2 \cdot - 7$

Multiply $- 10$ by $- 2$ .

$- 3 x^{3} - 30 x^{2} - 21 x + 2 x^{2} + 20 x - 2 \cdot - 7$

Multiply $- 2$ by $- 7$ .

$- 3 x^{3} - 30 x^{2} - 21 x + 2 x^{2} + 20 x + 14$

Simplify by adding terms.

Add $- 30 x^{2}$ and $2 x^{2}$ .

$- 3 x^{3} - 28 x^{2} - 21 x + 20 x + 14$

Add $- 21 x$ and $20 x$ .

$- 3 x^{3} - 28 x^{2} - x + 14$

Write in Standard Form (3x-2)(-x^2-10x-7)

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