Write in Standard Form (4x-9)(2x^2+2x+1)

$(4 x - 9) (2 x^{2} + 2 x + 1)$

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 $(4 x - 9) (2 x^{2} + 2 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$4 x (2 x^{2}) + 4 x (2 x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x \cdot x^{2} + 4 x (2 x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

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

Move $x^{2}$ .

$4 \cdot 2 (x^{2} x) + 4 x (2 x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

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

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

$4 \cdot 2 (x^{2} x^{1}) + 4 x (2 x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

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

$4 \cdot 2 x^{2 + 1} + 4 x (2 x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Add $2$ and $1$ .

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

Multiply $4$ by $2$ .

$8 x^{3} + 4 x (2 x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Rewrite using the commutative property of multiplication.

$8 x^{3} + 4 \cdot 2 x \cdot x + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

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

Move $x$ .

$8 x^{3} + 4 \cdot 2 (x \cdot x) + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Multiply $x$ by $x$ .

$8 x^{3} + 4 \cdot 2 x^{2} + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Multiply $4$ by $2$ .

$8 x^{3} + 8 x^{2} + 4 x \cdot 1 - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Multiply $4$ by $1$ .

$8 x^{3} + 8 x^{2} + 4 x - 9 (2 x^{2}) - 9 (2 x) - 9 \cdot 1$

Multiply $2$ by $- 9$ .

$8 x^{3} + 8 x^{2} + 4 x - 18 x^{2} - 9 (2 x) - 9 \cdot 1$

Multiply $2$ by $- 9$ .

$8 x^{3} + 8 x^{2} + 4 x - 18 x^{2} - 18 x - 9 \cdot 1$

Multiply $- 9$ by $1$ .

$8 x^{3} + 8 x^{2} + 4 x - 18 x^{2} - 18 x - 9$

Simplify by adding terms.

Subtract $18 x^{2}$ from $8 x^{2}$ .

$8 x^{3} - 10 x^{2} + 4 x - 18 x - 9$

Subtract $18 x$ from $4 x$ .

$8 x^{3} - 10 x^{2} - 14 x - 9$

Write in Standard Form (4x-9)(2x^2+2x+1)

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