Write in Standard Form (4x-3)(-2x^2-7x-5)

$(4 x - 3) (- 2 x^{2} - 7 x - 5)$

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 $(4 x - 3) (- 2 x^{2} - 7 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $4$ by $- 2$ .

$- 8 x^{3} + 4 x (- 7 x) + 4 x \cdot - 5 - 3 (- 2 x^{2}) - 3 (- 7 x) - 3 \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 8 x^{3} + 4 \cdot - 7 x \cdot x + 4 x \cdot - 5 - 3 (- 2 x^{2}) - 3 (- 7 x) - 3 \cdot - 5$

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

Move $x$ .

$- 8 x^{3} + 4 \cdot - 7 (x \cdot x) + 4 x \cdot - 5 - 3 (- 2 x^{2}) - 3 (- 7 x) - 3 \cdot - 5$

Multiply $x$ by $x$ .

$- 8 x^{3} + 4 \cdot - 7 x^{2} + 4 x \cdot - 5 - 3 (- 2 x^{2}) - 3 (- 7 x) - 3 \cdot - 5$

Multiply $4$ by $- 7$ .

$- 8 x^{3} - 28 x^{2} + 4 x \cdot - 5 - 3 (- 2 x^{2}) - 3 (- 7 x) - 3 \cdot - 5$

Multiply $- 5$ by $4$ .

$- 8 x^{3} - 28 x^{2} - 20 x - 3 (- 2 x^{2}) - 3 (- 7 x) - 3 \cdot - 5$

Multiply $- 2$ by $- 3$ .

$- 8 x^{3} - 28 x^{2} - 20 x + 6 x^{2} - 3 (- 7 x) - 3 \cdot - 5$

Multiply $- 7$ by $- 3$ .

$- 8 x^{3} - 28 x^{2} - 20 x + 6 x^{2} + 21 x - 3 \cdot - 5$

Multiply $- 3$ by $- 5$ .

$- 8 x^{3} - 28 x^{2} - 20 x + 6 x^{2} + 21 x + 15$

Simplify by adding terms.

Add $- 28 x^{2}$ and $6 x^{2}$ .

$- 8 x^{3} - 22 x^{2} - 20 x + 21 x + 15$

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

$- 8 x^{3} - 22 x^{2} + x + 15$

Write in Standard Form (4x-3)(-2x^2-7x-5)

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