# Multiply (4r^2-t-5)(3t^2+4t-1)

(4r2-t-5)(3t2+4t-1)
Expand (4r2-t-5)(3t2+4t-1) by multiplying each term in the first expression by each term in the second expression.
4r2(3t2)+4r2(4t)+4r2⋅-1-t(3t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Simplify terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
4⋅3(r2t2)+4r2(4t)+4r2⋅-1-t(3t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply 4 by 3.
12(r2t2)+4r2(4t)+4r2⋅-1-t(3t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Rewrite using the commutative property of multiplication.
12r2t2+4⋅4(r2t)+4r2⋅-1-t(3t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply 4 by 4.
12r2t2+16(r2t)+4r2⋅-1-t(3t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply -1 by 4.
12r2t2+16r2t-4r2-t(3t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Rewrite using the commutative property of multiplication.
12r2t2+16r2t-4r2-1⋅3(t⋅t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply t by t2 by adding the exponents.
Multiply t by t2.
Raise t to the power of 1.
12r2t2+16r2t-4r2-1⋅3(t1t2)-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Use the power rule aman=am+n to combine exponents.
12r2t2+16r2t-4r2-1⋅3t1+2-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
12r2t2+16r2t-4r2-1⋅3t1+2-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
12r2t2+16r2t-4r2-1⋅3t3-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
12r2t2+16r2t-4r2-1⋅3t3-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply -1 by 3.
12r2t2+16r2t-4r2-3t3-t(4t)-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply t by t.
12r2t2+16r2t-4r2-3t3-1⋅4t2-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply -1 by 4.
12r2t2+16r2t-4r2-3t3-4t2-t⋅-1-5(3t2)-5(4t)-5⋅-1
Multiply -t⋅-1.
Multiply -1 by -1.
12r2t2+16r2t-4r2-3t3-4t2+1t-5(3t2)-5(4t)-5⋅-1
Multiply t by 1.
12r2t2+16r2t-4r2-3t3-4t2+t-5(3t2)-5(4t)-5⋅-1
12r2t2+16r2t-4r2-3t3-4t2+t-5(3t2)-5(4t)-5⋅-1
Multiply 3 by -5.
12r2t2+16r2t-4r2-3t3-4t2+t-15t2-5(4t)-5⋅-1
Multiply 4 by -5.
12r2t2+16r2t-4r2-3t3-4t2+t-15t2-20t-5⋅-1
Multiply -5 by -1.
12r2t2+16r2t-4r2-3t3-4t2+t-15t2-20t+5
12r2t2+16r2t-4r2-3t3-4t2+t-15t2-20t+5
Subtract 15t2 from -4t2.
12r2t2+16r2t-4r2-3t3-19t2+t-20t+5
Subtract 20t from t.
12r2t2+16r2t-4r2-3t3-19t2-19t+5
Move -4r2.
12r2t2+16r2t-3t3-4r2-19t2-19t+5
12r2t2+16r2t-3t3-4r2-19t2-19t+5
12r2t2+16r2t-3t3-4r2-19t2-19t+5
Multiply (4r^2-t-5)(3t^2+4t-1)

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