Simplify (4x+7y)(4x-7y)

$(4 x + 7 y) (4 x - 7 y)$

Step 1

Expand $(4 x + 7 y) (4 x - 7 y)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 7 y) + 7 y (4 x - 7 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 7 y) + 7 y (4 x - 7 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 7 y) + 7 y (4 x) + 7 y (- 7 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x (- 7 y) + 7 y (4 x) + 7 y (- 7 y)$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x (- 7 y) + 7 y (4 x) + 7 y (- 7 y)$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x (- 7 y) + 7 y (4 x) + 7 y (- 7 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} + 4 \cdot - 7 x y + 7 y (4 x) + 7 y (- 7 y)$

Multiply $4$ by $- 7$ .

$16 x^{2} - 28 x y + 7 y (4 x) + 7 y (- 7 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 28 x y + 7 \cdot 4 y x + 7 y (- 7 y)$

Multiply $7$ by $4$ .

$16 x^{2} - 28 x y + 28 y x + 7 y (- 7 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 28 x y + 28 y x + 7 \cdot - 7 y \cdot y$

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

Move $y$ .

$16 x^{2} - 28 x y + 28 y x + 7 \cdot - 7 (y \cdot y)$

Multiply $y$ by $y$ .

$16 x^{2} - 28 x y + 28 y x + 7 \cdot - 7 y^{2}$

Multiply $7$ by $- 7$ .

$16 x^{2} - 28 x y + 28 y x - 49 y^{2}$

Add $- 28 x y$ and $28 y x$ .

Move $y$ .

$16 x^{2} - 28 x y + 28 x y - 49 y^{2}$

Add $- 28 x y$ and $28 x y$ .

$16 x^{2} + 0 - 49 y^{2}$

Add $16 x^{2}$ and $0$ .

$16 x^{2} - 49 y^{2}$