Simplify (9z-u)(4z+7u)

$(9 z - u) (4 z + 7 u)$

Step 1

Expand

$(9 z - u) (4 z + 7 u)$ using the FOIL Method.

Apply the distributive property.

$9 z (4 z + 7 u) - u (4 z + 7 u)$

Apply the distributive property.

$9 z (4 z) + 9 z (7 u) - u (4 z + 7 u)$

Apply the distributive property.

$9 z (4 z) + 9 z (7 u) - u (4 z) - u (7 u)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 \cdot 4 z \cdot z + 9 z (7 u) - u (4 z) - u (7 u)$

Multiply

$z$ by

$z$ by adding the exponents.

Move

$z$ .

$9 \cdot 4 (z \cdot z) + 9 z (7 u) - u (4 z) - u (7 u)$

Multiply

$z$ by

$z$ .

$9 \cdot 4 z^{2} + 9 z (7 u) - u (4 z) - u (7 u)$

Multiply

$9$ by

$4$ .

$36 z^{2} + 9 z (7 u) - u (4 z) - u (7 u)$

Rewrite using the commutative property of multiplication.

$36 z^{2} + 9 \cdot 7 z u - u (4 z) - u (7 u)$

Multiply

$9$ by

$7$ .

$36 z^{2} + 63 z u - u (4 z) - u (7 u)$

Rewrite using the commutative property of multiplication.

$36 z^{2} + 63 z u - 1 \cdot 4 u z - u (7 u)$

Multiply

$- 1$ by

$4$ .

$36 z^{2} + 63 z u - 4 u z - u (7 u)$

Rewrite using the commutative property of multiplication.

$36 z^{2} + 63 z u - 4 u z - 1 \cdot 7 u \cdot u$

Multiply

$u$ by

$u$ by adding the exponents.

Move

$u$ .

$36 z^{2} + 63 z u - 4 u z - 1 \cdot 7 (u \cdot u)$

Multiply

$u$ by

$u$ .

$36 z^{2} + 63 z u - 4 u z - 1 \cdot 7 u^{2}$

Multiply

$- 1$ by

$7$ .

$36 z^{2} + 63 z u - 4 u z - 7 u^{2}$

Subtract

$4 u z$ from

$63 z u$ .

Move

$z$ .

$36 z^{2} + 63 u z - 4 u z - 7 u^{2}$

Subtract

$4 u z$ from

$63 u z$ .

$36 z^{2} + 59 u z - 7 u^{2}$

Step 3

Move

$36 z^{2}$ .

$59 u z - 7 u^{2} + 36 z^{2}$

Step 4

Reorder

$59 u z$ and

$- 7 u^{2}$ .

$- 7 u^{2} + 59 u z + 36 z^{2}$

Simplify (9z-u)(4z+7u)

Related Questions