Find the Product (7x^2-3)(8x^2-7x+5)

$(7 x^{2} - 3) (8 x^{2} - 7 x + 5)$

Expand $(7 x^{2} - 3) (8 x^{2} - 7 x + 5)$ by multiplying each term in the first expression by each term in the second expression.

$7 x^{2} (8 x^{2}) + 7 x^{2} (- 7 x) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 8 x^{2} x^{2} + 7 x^{2} (- 7 x) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

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

Move $x^{2}$ .

$7 \cdot 8 (x^{2} x^{2}) + 7 x^{2} (- 7 x) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

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

$7 \cdot 8 x^{2 + 2} + 7 x^{2} (- 7 x) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Add $2$ and $2$ .

$7 \cdot 8 x^{4} + 7 x^{2} (- 7 x) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Multiply $7$ by $8$ .

$56 x^{4} + 7 x^{2} (- 7 x) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Rewrite using the commutative property of multiplication.

$56 x^{4} + 7 \cdot - 7 x^{2} x + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

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

Move $x$ .

$56 x^{4} + 7 \cdot - 7 (x \cdot x^{2}) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

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

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

$56 x^{4} + 7 \cdot - 7 (x^{1} x^{2}) + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

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

$56 x^{4} + 7 \cdot - 7 x^{1 + 2} + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Add $1$ and $2$ .

$56 x^{4} + 7 \cdot - 7 x^{3} + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Multiply $7$ by $- 7$ .

$56 x^{4} - 49 x^{3} + 7 x^{2} \cdot 5 - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Multiply $5$ by $7$ .

$56 x^{4} - 49 x^{3} + 35 x^{2} - 3 (8 x^{2}) - 3 (- 7 x) - 3 \cdot 5$

Multiply $8$ by $- 3$ .

$56 x^{4} - 49 x^{3} + 35 x^{2} - 24 x^{2} - 3 (- 7 x) - 3 \cdot 5$

Multiply $- 7$ by $- 3$ .

$56 x^{4} - 49 x^{3} + 35 x^{2} - 24 x^{2} + 21 x - 3 \cdot 5$

Multiply $- 3$ by $5$ .

$56 x^{4} - 49 x^{3} + 35 x^{2} - 24 x^{2} + 21 x - 15$

Subtract $24 x^{2}$ from $35 x^{2}$ .

$56 x^{4} - 49 x^{3} + 11 x^{2} + 21 x - 15$