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

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

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

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

Step 3

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} (- 3 x) + x^{2} \cdot - 4 + 3 x \cdot x^{2} + 3 x (- 3 x) + 3 x \cdot - 4 + 2 x^{2} + 2 (- 3 x) + 2 \cdot - 4$ .

Reorder the factors in the terms $x^{2} (- 3 x)$ and $3 x \cdot x^{2}$ .

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

Add $- 3 x^{2} x$ and $3 x^{2} x$ .

$x^{2} x^{2} + x^{2} \cdot - 4 + 0 + 3 x (- 3 x) + 3 x \cdot - 4 + 2 x^{2} + 2 (- 3 x) + 2 \cdot - 4$

Add $x^{2} x^{2} + x^{2} \cdot - 4$ and $0$ .

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

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Move $- 4$ to the left of $x^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $- 3$ .

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

Multiply $- 4$ by $3$ .

$x^{4} - 4 x^{2} - 9 x^{2} - 12 x + 2 x^{2} + 2 (- 3 x) + 2 \cdot - 4$

Multiply $- 3$ by $2$ .

$x^{4} - 4 x^{2} - 9 x^{2} - 12 x + 2 x^{2} - 6 x + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$x^{4} - 4 x^{2} - 9 x^{2} - 12 x + 2 x^{2} - 6 x - 8$

Simplify by adding terms.

Subtract $9 x^{2}$ from $- 4 x^{2}$ .

$x^{4} - 13 x^{2} - 12 x + 2 x^{2} - 6 x - 8$

Add $- 13 x^{2}$ and $2 x^{2}$ .

$x^{4} - 11 x^{2} - 12 x - 6 x - 8$

Subtract $6 x$ from $- 12 x$ .

$x^{4} - 11 x^{2} - 18 x - 8$

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

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