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Simplify (24z^5-16z^4)/(4z^2)

24z5-16z44z2

Step 1
Simplify terms.

Factor 8z4 out of 24z5-16z4.

Factor 8z4 out of 24z5.
8z4(3z)-16z44z2
Factor 8z4 out of -16z4.
8z4(3z)+8z4(-2)4z2
Factor 8z4 out of 8z4(3z)+8z4(-2).
8z4(3z-2)4z2
8z4(3z-2)4z2
Cancel the common factor of 8 and 4.

Factor 4 out of 8z4(3z-2).
4(2z4(3z-2))4z2
Cancel the common factors.

Factor 4 out of 4z2.
4(2z4(3z-2))4(z2)
Cancel the common factor.
4(2z4(3z-2))4z2
Rewrite the expression.
2z4(3z-2)z2
2z4(3z-2)z2
2z4(3z-2)z2
Cancel the common factor of z4 and z2.

Factor z2 out of 2z4(3z-2).
z2(2z2(3z-2))z2
Cancel the common factors.

Multiply by 1.
z2(2z2(3z-2))z21
Cancel the common factor.
z2(2z2(3z-2))z21
Rewrite the expression.
2z2(3z-2)1
Divide 2z2(3z-2) by 1.
2z2(3z-2)
2z2(3z-2)
2z2(3z-2)
Apply the distributive property.
2z2(3z)+2z2-2
Simplify the expression.

Rewrite using the commutative property of multiplication.
23z2z+2z2-2
Multiply -2 by 2.
23z2z-4z2
23z2z-4z2
23z2z-4z2

Step 2
Simplify each term.

Multiply z2 by z by adding the exponents.

Move z.
23(zz2)-4z2
Multiply z by z2.

Raise z to the power of 1.
23(z1z2)-4z2
Use the power rule aman=am+n to combine exponents.
23z1+2-4z2
23z1+2-4z2
Add 1 and 2.
23z3-4z2
23z3-4z2
Multiply 2 by 3.
6z3-4z2
6z3-4z2