Write in Standard Form 4(2-3w)(w^2-2w+10)

$4 (2 - 3 w) (w^{2} - 2 w + 10)$

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

Simplify by multiplying through.

Apply the distributive property.

$(4 \cdot 2 + 4 (- 3 w)) (w^{2} - 2 w + 10)$

Multiply.

Multiply $4$ by $2$ .

$(8 + 4 (- 3 w)) (w^{2} - 2 w + 10)$

Multiply $- 3$ by $4$ .

$(8 - 12 w) (w^{2} - 2 w + 10)$

Step 3

Expand $(8 - 12 w) (w^{2} - 2 w + 10)$ by multiplying each term in the first expression by each term in the second expression.

$8 w^{2} + 8 (- 2 w) + 8 \cdot 10 - 12 w \cdot w^{2} - 12 w (- 2 w) - 12 w \cdot 10$

Step 4

Simplify terms.

Simplify each term.

Multiply $- 2$ by $8$ .

$8 w^{2} - 16 w + 8 \cdot 10 - 12 w \cdot w^{2} - 12 w (- 2 w) - 12 w \cdot 10$

Multiply $8$ by $10$ .

$8 w^{2} - 16 w + 80 - 12 w \cdot w^{2} - 12 w (- 2 w) - 12 w \cdot 10$

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

Move $w^{2}$ .

$8 w^{2} - 16 w + 80 - 12 (w^{2} w) - 12 w (- 2 w) - 12 w \cdot 10$

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

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

$8 w^{2} - 16 w + 80 - 12 (w^{2} w^{1}) - 12 w (- 2 w) - 12 w \cdot 10$

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

$8 w^{2} - 16 w + 80 - 12 w^{2 + 1} - 12 w (- 2 w) - 12 w \cdot 10$

Add $2$ and $1$ .

$8 w^{2} - 16 w + 80 - 12 w^{3} - 12 w (- 2 w) - 12 w \cdot 10$

Rewrite using the commutative property of multiplication.

$8 w^{2} - 16 w + 80 - 12 w^{3} - 12 \cdot - 2 w \cdot w - 12 w \cdot 10$

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

$8 w^{2} - 16 w + 80 - 12 w^{3} - 12 \cdot - 2 (w \cdot w) - 12 w \cdot 10$

Multiply $w$ by $w$ .

$8 w^{2} - 16 w + 80 - 12 w^{3} - 12 \cdot - 2 w^{2} - 12 w \cdot 10$

Multiply $- 12$ by $- 2$ .

$8 w^{2} - 16 w + 80 - 12 w^{3} + 24 w^{2} - 12 w \cdot 10$

Multiply $10$ by $- 12$ .

$8 w^{2} - 16 w + 80 - 12 w^{3} + 24 w^{2} - 120 w$

Simplify by adding terms.

Add $8 w^{2}$ and $24 w^{2}$ .

$32 w^{2} - 16 w + 80 - 12 w^{3} - 120 w$

Subtract $120 w$ from $- 16 w$ .

$32 w^{2} - 136 w + 80 - 12 w^{3}$

Simplify the expression.

Move $80$ .

$32 w^{2} - 136 w - 12 w^{3} + 80$

Move $- 136 w$ .

$32 w^{2} - 12 w^{3} - 136 w + 80$

Reorder $32 w^{2}$ and $- 12 w^{3}$ .

$- 12 w^{3} + 32 w^{2} - 136 w + 80$

Write in Standard Form 4(2-3w)(w^2-2w+10)

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