(4t-5)(t3+4t2)

Apply the distributive property.

4t(t3+4t2)-5(t3+4t2)

Apply the distributive property.

4t⋅t3+4t(4t2)-5(t3+4t2)

Apply the distributive property.

4t⋅t3+4t(4t2)-5t3-5(4t2)

4t⋅t3+4t(4t2)-5t3-5(4t2)

Simplify each term.

Multiply t by t3 by adding the exponents.

Move t3.

4(t3t)+4t(4t2)-5t3-5(4t2)

Multiply t3 by t.

Raise t to the power of 1.

4(t3t1)+4t(4t2)-5t3-5(4t2)

Use the power rule aman=am+n to combine exponents.

4t3+1+4t(4t2)-5t3-5(4t2)

4t3+1+4t(4t2)-5t3-5(4t2)

Add 3 and 1.

4t4+4t(4t2)-5t3-5(4t2)

4t4+4t(4t2)-5t3-5(4t2)

Rewrite using the commutative property of multiplication.

4t4+4⋅4(t⋅t2)-5t3-5(4t2)

Multiply t by t2 by adding the exponents.

Multiply t by t2.

Raise t to the power of 1.

4t4+4⋅4(t1t2)-5t3-5(4t2)

Use the power rule aman=am+n to combine exponents.

4t4+4⋅4t1+2-5t3-5(4t2)

4t4+4⋅4t1+2-5t3-5(4t2)

Add 1 and 2.

4t4+4⋅4t3-5t3-5(4t2)

4t4+4⋅4t3-5t3-5(4t2)

Multiply 4 by 4.

4t4+16t3-5t3-5(4t2)

Multiply 4 by -5.

4t4+16t3-5t3-20t2

4t4+16t3-5t3-20t2

Subtract 5t3 from 16t3.

4t4+11t3-20t2

4t4+11t3-20t2

Simplify (4t-5)(t^3+4t^2)