Write in Standard Form (3x^2-2x+1)(x^2+x-4)

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

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 $(3 x^{2} - 2 x + 1) (x^{2} + x - 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $- 4$ by $3$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

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

Move $x^{2}$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 (x^{2} x) - 2 x \cdot x - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

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

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

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 (x^{2} x^{1}) - 2 x \cdot x - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

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

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{2 + 1} - 2 x \cdot x - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

Add $2$ and $1$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 x \cdot x - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

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

Move $x$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 (x \cdot x) - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

Multiply $x$ by $x$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 x^{2} - 2 x \cdot - 4 + 1 x^{2} + 1 x + 1 \cdot - 4$

Multiply $- 4$ by $- 2$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 x^{2} + 8 x + 1 x^{2} + 1 x + 1 \cdot - 4$

Multiply $x^{2}$ by $1$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 x^{2} + 8 x + x^{2} + 1 x + 1 \cdot - 4$

Multiply $x$ by $1$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 x^{2} + 8 x + x^{2} + x + 1 \cdot - 4$

Multiply $- 4$ by $1$ .

$3 x^{4} + 3 x^{3} - 12 x^{2} - 2 x^{3} - 2 x^{2} + 8 x + x^{2} + x - 4$

Simplify by adding terms.

Subtract $2 x^{3}$ from $3 x^{3}$ .

$3 x^{4} + x^{3} - 12 x^{2} - 2 x^{2} + 8 x + x^{2} + x - 4$

Subtract $2 x^{2}$ from $- 12 x^{2}$ .

$3 x^{4} + x^{3} - 14 x^{2} + 8 x + x^{2} + x - 4$

Add $- 14 x^{2}$ and $x^{2}$ .

$3 x^{4} + x^{3} - 13 x^{2} + 8 x + x - 4$

Add $8 x$ and $x$ .

$3 x^{4} + x^{3} - 13 x^{2} + 9 x - 4$

Write in Standard Form (3x^2-2x+1)(x^2+x-4)

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