Write in Standard Form (3x-2)(x^2-2x+1)

$(3 x - 2) (x^{2} - 2 x + 1)$

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

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

Step 3

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $- 2$ .

$3 x^{3} - 6 x^{2} + 3 x \cdot 1 - 2 x^{2} - 2 (- 2 x) - 2 \cdot 1$

Multiply $3$ by $1$ .

$3 x^{3} - 6 x^{2} + 3 x - 2 x^{2} - 2 (- 2 x) - 2 \cdot 1$

Multiply $- 2$ by $- 2$ .

$3 x^{3} - 6 x^{2} + 3 x - 2 x^{2} + 4 x - 2 \cdot 1$

Multiply $- 2$ by $1$ .

$3 x^{3} - 6 x^{2} + 3 x - 2 x^{2} + 4 x - 2$

Simplify by adding terms.

Subtract $2 x^{2}$ from $- 6 x^{2}$ .

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

Add $3 x$ and $4 x$ .

$3 x^{3} - 8 x^{2} + 7 x - 2$