Simplify (2y-7)^2

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

Step 1

Rewrite ${(2 y - 7)}^{2}$ as $(2 y - 7) (2 y - 7)$ .

$(2 y - 7) (2 y - 7)$

Step 2

Expand $(2 y - 7) (2 y - 7)$ using the FOIL Method.

Apply the distributive property.

$2 y (2 y - 7) - 7 (2 y - 7)$

Apply the distributive property.

$2 y (2 y) + 2 y \cdot - 7 - 7 (2 y - 7)$

Apply the distributive property.

$2 y (2 y) + 2 y \cdot - 7 - 7 (2 y) - 7 \cdot - 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 y \cdot y + 2 y \cdot - 7 - 7 (2 y) - 7 \cdot - 7$

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

Move $y$ .

$2 \cdot 2 (y \cdot y) + 2 y \cdot - 7 - 7 (2 y) - 7 \cdot - 7$

Multiply $y$ by $y$ .

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

Multiply $2$ by $2$ .

$4 y^{2} + 2 y \cdot - 7 - 7 (2 y) - 7 \cdot - 7$

Multiply $- 7$ by $2$ .

$4 y^{2} - 14 y - 7 (2 y) - 7 \cdot - 7$

Multiply $2$ by $- 7$ .

$4 y^{2} - 14 y - 14 y - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$4 y^{2} - 14 y - 14 y + 49$

Subtract $14 y$ from $- 14 y$ .

$4 y^{2} - 28 y + 49$