Simplify (x^2-x+9)(x^2+x+15)

$(x^{2} - x + 9) (x^{2} + x + 15)$

Step 1

Expand $(x^{2} - x + 9) (x^{2} + x + 15)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x^{2} + x^{2} x + x^{2} \cdot 15 - x \cdot x^{2} - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} x + x^{2} \cdot 15 - x \cdot x^{2} - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$ .

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

$x^{2} x^{2} + x^{2} x + x^{2} \cdot 15 - x^{2} x - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

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

$x^{2} x^{2} + x^{2} \cdot 15 + 0 - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

Add $x^{2} x^{2} + x^{2} \cdot 15$ and $0$ .

$x^{2} x^{2} + x^{2} \cdot 15 - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

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.

$x^{2 + 2} + x^{2} \cdot 15 - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

Add $2$ and $2$ .

$x^{4} + x^{2} \cdot 15 - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

Move $15$ to the left of $x^{2}$ .

$x^{4} + 15 \cdot x^{2} - x \cdot x - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

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

Move $x$ .

$x^{4} + 15 x^{2} - (x \cdot x) - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

Multiply $x$ by $x$ .

$x^{4} + 15 x^{2} - x^{2} - x \cdot 15 + 9 x^{2} + 9 x + 9 \cdot 15$

Multiply $15$ by $- 1$ .

$x^{4} + 15 x^{2} - x^{2} - 15 x + 9 x^{2} + 9 x + 9 \cdot 15$

Multiply $9$ by $15$ .

$x^{4} + 15 x^{2} - x^{2} - 15 x + 9 x^{2} + 9 x + 135$

Simplify by adding terms.

Subtract $x^{2}$ from $15 x^{2}$ .

$x^{4} + 14 x^{2} - 15 x + 9 x^{2} + 9 x + 135$

Add $14 x^{2}$ and $9 x^{2}$ .

$x^{4} + 23 x^{2} - 15 x + 9 x + 135$

Add $- 15 x$ and $9 x$ .

$x^{4} + 23 x^{2} - 6 x + 135$