# Simplify (5u+4v)(3u+6v-1)

(5u+4v)(3u+6v-1)
Expand (5u+4v)(3u+6v-1) by multiplying each term in the first expression by each term in the second expression.
5u(3u)+5u(6v)+5u⋅-1+4v(3u)+4v(6v)+4v⋅-1
Simplify each term.
Multiply u by u.
5⋅3u2+5u(6v)+5u⋅-1+4v(3u)+4v(6v)+4v⋅-1
Multiply 5 by 3.
15u2+5u(6v)+5u⋅-1+4v(3u)+4v(6v)+4v⋅-1
Rewrite using the commutative property of multiplication.
15u2+5⋅6(uv)+5u⋅-1+4v(3u)+4v(6v)+4v⋅-1
Multiply 5 by 6.
15u2+30(uv)+5u⋅-1+4v(3u)+4v(6v)+4v⋅-1
Multiply -1 by 5.
15u2+30uv-5u+4v(3u)+4v(6v)+4v⋅-1
Rewrite using the commutative property of multiplication.
15u2+30uv-5u+4⋅3(vu)+4v(6v)+4v⋅-1
Multiply 4 by 3.
15u2+30uv-5u+12(vu)+4v(6v)+4v⋅-1
Multiply v by v.
15u2+30uv-5u+12vu+4⋅6v2+4v⋅-1
Multiply 4 by 6.
15u2+30uv-5u+12vu+24v2+4v⋅-1
Multiply -1 by 4.
15u2+30uv-5u+12vu+24v2-4v
15u2+30uv-5u+12vu+24v2-4v
Move v.
15u2+30uv+12uv-5u+24v2-4v
15u2+42uv-5u+24v2-4v
15u2+42uv-5u+24v2-4v
Move -5u.
15u2+42uv+24v2-5u-4v
Simplify (5u+4v)(3u+6v-1)

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