Find the Product (x^6-4)(x^2-7x+5)

$(x^{6} - 4) (x^{2} - 7 x + 5)$

Step 1

Expand $(x^{6} - 4) (x^{2} - 7 x + 5)$ by multiplying each term in the first expression by each term in the second expression.

$x^{6} x^{2} + x^{6} (- 7 x) + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Step 2

Simplify each term.

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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

$x^{6 + 2} + x^{6} (- 7 x) + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Add $6$ and $2$ .

$x^{8} + x^{6} (- 7 x) + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Rewrite using the commutative property of multiplication.

$x^{8} - 7 x^{6} x + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Multiply $x^{6}$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 7 (x \cdot x^{6}) + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Multiply $x$ by $x^{6}$ .

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

$x^{8} - 7 (x^{1} x^{6}) + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

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

$x^{8} - 7 x^{1 + 6} + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Add $1$ and $6$ .

$x^{8} - 7 x^{7} + x^{6} \cdot 5 - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Move $5$ to the left of $x^{6}$ .

$x^{8} - 7 x^{7} + 5 \cdot x^{6} - 4 x^{2} - 4 (- 7 x) - 4 \cdot 5$

Multiply $- 7$ by $- 4$ .

$x^{8} - 7 x^{7} + 5 x^{6} - 4 x^{2} + 28 x - 4 \cdot 5$

Multiply $- 4$ by $5$ .

$x^{8} - 7 x^{7} + 5 x^{6} - 4 x^{2} + 28 x - 20$