Simplify (yz)(12xy-25xz-4y^2)

$(y z) (12 x y - 25 x z - 4 y^{2})$

Step 1

Apply the distributive property.

$y z (12 x y) + y z (- 25 x z) + y z (- 4 y^{2})$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$12 y z (x y) + y z (- 25 x z) + y z (- 4 y^{2})$

Rewrite using the commutative property of multiplication.

$12 y z (x y) - 25 y z (x z) + y z (- 4 y^{2})$

Rewrite using the commutative property of multiplication.

$12 y z (x y) - 25 y z (x z) - 4 y z y^{2}$

Step 3

Simplify each term.

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

Move $y$ .

$12 (y \cdot y) z x - 25 y z (x z) - 4 y z y^{2}$

Multiply $y$ by $y$ .

$12 y^{2} z x - 25 y z (x z) - 4 y z y^{2}$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$12 y^{2} z x - 25 y (z \cdot z) x - 4 y z y^{2}$

Multiply $z$ by $z$ .

$12 y^{2} z x - 25 y z^{2} x - 4 y z y^{2}$

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

Move $y^{2}$ .

$12 y^{2} z x - 25 y z^{2} x - 4 (y^{2} y) z$

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

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

$12 y^{2} z x - 25 y z^{2} x - 4 (y^{2} y^{1}) z$

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

$12 y^{2} z x - 25 y z^{2} x - 4 y^{2 + 1} z$

Add $2$ and $1$ .

$12 y^{2} z x - 25 y z^{2} x - 4 y^{3} z$