# Simplify 1/4*(n(-24+8m-100p))

14⋅(n(-24+8m-100p))
Apply the distributive property.
14⋅(n⋅-24+n(8m)+n(-100p))
Simplify.
Move -24 to the left of n.
14⋅(-24⋅n+n(8m)+n(-100p))
Rewrite using the commutative property of multiplication.
14⋅(-24⋅n+8nm+n(-100p))
Rewrite using the commutative property of multiplication.
14⋅(-24⋅n+8nm-100np)
14⋅(-24⋅n+8nm-100np)
Apply the distributive property.
14(-24n)+14(8nm)+14(-100np)
Simplify.
Cancel the common factor of 4.
Factor 4 out of -24n.
14(4(-6n))+14(8nm)+14(-100np)
Cancel the common factor.
14(4(-6n))+14(8nm)+14(-100np)
Rewrite the expression.
-6n+14(8nm)+14(-100np)
-6n+14(8nm)+14(-100np)
Cancel the common factor of 4.
Factor 4 out of 8nm.
-6n+14(4(2nm))+14(-100np)
Cancel the common factor.
-6n+14(4(2nm))+14(-100np)
Rewrite the expression.
-6n+2nm+14(-100np)
-6n+2nm+14(-100np)
Cancel the common factor of 4.
Factor 4 out of -100np.
-6n+2nm+14(4(-25np))
Cancel the common factor.
-6n+2nm+14(4(-25np))
Rewrite the expression.
-6n+2nm-25np
-6n+2nm-25np
-6n+2nm-25np
Move n.
-6n+2mn-25np
Move -6n.
2mn-25np-6n
Simplify 1/4*(n(-24+8m-100p))

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