Simplify (y^2-2y+7)(7y-3)

$(y^{2} - 2 y + 7) (7 y - 3)$

Step 1

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

$y^{2} (7 y) + y^{2} \cdot - 3 - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 y^{2} y + y^{2} \cdot - 3 - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

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

Move $y$ .

$7 (y \cdot y^{2}) + y^{2} \cdot - 3 - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

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

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

$7 (y^{1} y^{2}) + y^{2} \cdot - 3 - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

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

$7 y^{1 + 2} + y^{2} \cdot - 3 - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Add $1$ and $2$ .

$7 y^{3} + y^{2} \cdot - 3 - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Move $- 3$ to the left of $y^{2}$ .

$7 y^{3} - 3 \cdot y^{2} - 2 y (7 y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Rewrite using the commutative property of multiplication.

$7 y^{3} - 3 y^{2} - 2 \cdot 7 y \cdot y - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$7 y^{3} - 3 y^{2} - 2 \cdot 7 (y \cdot y) - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Multiply $y$ by $y$ .

$7 y^{3} - 3 y^{2} - 2 \cdot 7 y^{2} - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Multiply $- 2$ by $7$ .

$7 y^{3} - 3 y^{2} - 14 y^{2} - 2 y \cdot - 3 + 7 (7 y) + 7 \cdot - 3$

Multiply $- 3$ by $- 2$ .

$7 y^{3} - 3 y^{2} - 14 y^{2} + 6 y + 7 (7 y) + 7 \cdot - 3$

Multiply $7$ by $7$ .

$7 y^{3} - 3 y^{2} - 14 y^{2} + 6 y + 49 y + 7 \cdot - 3$

Multiply $7$ by $- 3$ .

$7 y^{3} - 3 y^{2} - 14 y^{2} + 6 y + 49 y - 21$

Simplify by adding terms.

Subtract $14 y^{2}$ from $- 3 y^{2}$ .

$7 y^{3} - 17 y^{2} + 6 y + 49 y - 21$

Add $6 y$ and $49 y$ .

$7 y^{3} - 17 y^{2} + 55 y - 21$