Expand the Trigonometric Expression (4m-7p)(4m-7p)

$(4 m - 7 p) (4 m - 7 p)$

Step 1

Expand $(4 m - 7 p) (4 m - 7 p)$ using the FOIL Method.

Apply the distributive property.

$4 m (4 m - 7 p) - 7 p (4 m - 7 p)$

Apply the distributive property.

$4 m (4 m) + 4 m (- 7 p) - 7 p (4 m - 7 p)$

Apply the distributive property.

$4 m (4 m) + 4 m (- 7 p) - 7 p (4 m) - 7 p (- 7 p)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 m \cdot m + 4 m (- 7 p) - 7 p (4 m) - 7 p (- 7 p)$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$4 \cdot 4 (m \cdot m) + 4 m (- 7 p) - 7 p (4 m) - 7 p (- 7 p)$

Multiply $m$ by $m$ .

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

Multiply $4$ by $4$ .

$16 m^{2} + 4 m (- 7 p) - 7 p (4 m) - 7 p (- 7 p)$

Rewrite using the commutative property of multiplication.

$16 m^{2} + 4 \cdot - 7 m p - 7 p (4 m) - 7 p (- 7 p)$

Multiply $4$ by $- 7$ .

$16 m^{2} - 28 m p - 7 p (4 m) - 7 p (- 7 p)$

Rewrite using the commutative property of multiplication.

$16 m^{2} - 28 m p - 7 \cdot 4 p m - 7 p (- 7 p)$

Multiply $- 7$ by $4$ .

$16 m^{2} - 28 m p - 28 p m - 7 p (- 7 p)$

Rewrite using the commutative property of multiplication.

$16 m^{2} - 28 m p - 28 p m - 7 \cdot - 7 p \cdot p$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$16 m^{2} - 28 m p - 28 p m - 7 \cdot - 7 (p \cdot p)$

Multiply $p$ by $p$ .

$16 m^{2} - 28 m p - 28 p m - 7 \cdot - 7 p^{2}$

Multiply $- 7$ by $- 7$ .

$16 m^{2} - 28 m p - 28 p m + 49 p^{2}$

Subtract $28 p m$ from $- 28 m p$ .

Move $p$ .

$16 m^{2} - 28 m p - 28 m p + 49 p^{2}$

Subtract $28 m p$ from $- 28 m p$ .

$16 m^{2} - 56 m p + 49 p^{2}$