# Simplify (a-1)(2a+3)(4a-5) (a-1)(2a+3)(4a-5)
Expand (a-1)(2a+3) using the FOIL Method.
Apply the distributive property.
(a(2a+3)-1(2a+3))(4a-5)
Apply the distributive property.
(a(2a)+a⋅3-1(2a+3))(4a-5)
Apply the distributive property.
(a(2a)+a⋅3-1(2a)-1⋅3)(4a-5)
(a(2a)+a⋅3-1(2a)-1⋅3)(4a-5)
Simplify and combine like terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
(2a⋅a+a⋅3-1(2a)-1⋅3)(4a-5)
Multiply a by a by adding the exponents.
Move a.
(2(a⋅a)+a⋅3-1(2a)-1⋅3)(4a-5)
Multiply a by a.
(2a2+a⋅3-1(2a)-1⋅3)(4a-5)
(2a2+a⋅3-1(2a)-1⋅3)(4a-5)
Move 3 to the left of a.
(2a2+3⋅a-1(2a)-1⋅3)(4a-5)
Multiply 2 by -1.
(2a2+3a-2a-1⋅3)(4a-5)
Multiply -1 by 3.
(2a2+3a-2a-3)(4a-5)
(2a2+3a-2a-3)(4a-5)
Subtract 2a from 3a.
(2a2+a-3)(4a-5)
(2a2+a-3)(4a-5)
Expand (2a2+a-3)(4a-5) by multiplying each term in the first expression by each term in the second expression.
2a2(4a)+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
Simplify terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
2⋅4(a2a)+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
Multiply a2 by a by adding the exponents.
Multiply a2 by a.
Raise a to the power of 1.
2⋅4(a2a1)+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
Use the power rule aman=am+n to combine exponents.
2⋅4a2+1+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
2⋅4a2+1+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
2⋅4a3+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
2⋅4a3+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
Multiply 2 by 4.
8a3+2a2⋅-5+a(4a)+a⋅-5-3(4a)-3⋅-5
Multiply -5 by 2.
8a3-10a2+a(4a)+a⋅-5-3(4a)-3⋅-5
Rewrite using the commutative property of multiplication.
8a3-10a2+4a⋅a+a⋅-5-3(4a)-3⋅-5
Multiply a by a by adding the exponents.
Move a.
8a3-10a2+4(a⋅a)+a⋅-5-3(4a)-3⋅-5
Multiply a by a.
8a3-10a2+4a2+a⋅-5-3(4a)-3⋅-5
8a3-10a2+4a2+a⋅-5-3(4a)-3⋅-5
Move -5 to the left of a.
8a3-10a2+4a2-5⋅a-3(4a)-3⋅-5
Multiply 4 by -3.
8a3-10a2+4a2-5a-12a-3⋅-5
Multiply -3 by -5.
8a3-10a2+4a2-5a-12a+15
8a3-10a2+4a2-5a-12a+15