Find the Product (2x^2-4x+1)(5x-7)

$(2 x^{2} - 4 x + 1) (5 x - 7)$

Step 1

Expand $(2 x^{2} - 4 x + 1) (5 x - 7)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $5$ .

$10 x^{3} + 2 x^{2} \cdot - 7 - 4 x (5 x) - 4 x \cdot - 7 + 1 (5 x) + 1 \cdot - 7$

Multiply $- 7$ by $2$ .

$10 x^{3} - 14 x^{2} - 4 x (5 x) - 4 x \cdot - 7 + 1 (5 x) + 1 \cdot - 7$

Rewrite using the commutative property of multiplication.

$10 x^{3} - 14 x^{2} - 4 \cdot 5 x \cdot x - 4 x \cdot - 7 + 1 (5 x) + 1 \cdot - 7$

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

Move $x$ .

$10 x^{3} - 14 x^{2} - 4 \cdot 5 (x \cdot x) - 4 x \cdot - 7 + 1 (5 x) + 1 \cdot - 7$

Multiply $x$ by $x$ .

$10 x^{3} - 14 x^{2} - 4 \cdot 5 x^{2} - 4 x \cdot - 7 + 1 (5 x) + 1 \cdot - 7$

Multiply $- 4$ by $5$ .

$10 x^{3} - 14 x^{2} - 20 x^{2} - 4 x \cdot - 7 + 1 (5 x) + 1 \cdot - 7$

Multiply $- 7$ by $- 4$ .

$10 x^{3} - 14 x^{2} - 20 x^{2} + 28 x + 1 (5 x) + 1 \cdot - 7$

Multiply $5 x$ by $1$ .

$10 x^{3} - 14 x^{2} - 20 x^{2} + 28 x + 5 x + 1 \cdot - 7$

Multiply $- 7$ by $1$ .

$10 x^{3} - 14 x^{2} - 20 x^{2} + 28 x + 5 x - 7$

Simplify by adding terms.

Subtract $20 x^{2}$ from $- 14 x^{2}$ .

$10 x^{3} - 34 x^{2} + 28 x + 5 x - 7$

Add $28 x$ and $5 x$ .

$10 x^{3} - 34 x^{2} + 33 x - 7$