How do you simplify #(a^3+2a^2b-ab^2+3b^3)(4ab)#? Algebra Polynomials and Factoring Multiplication of Monomials by Polynomials 1 Answer Don't Memorise Aug 21, 2015 #=color(blue)(4a^4b + 4a^3b^2 +12ab^4# Explanation: #(a^3+2a^2b−ab^2+3b^3)color(blue)((4ab)# #=(a^3) * color(blue)((4ab)) +(2a^2b) * color(blue)((4ab)) - (ab^2) *color(blue)((4ab)) +(3b^3) .color(blue)((4ab)# #=4a^3*ab + 8a^2b*ab - 4ab^2*ab +12b^3*ab# By property #color(blue)(a^m*a^n=a^(m+n)# Applying the same to powers of #a# and #b# #=4a^((3+1))b + 8a^((2+1))b^((1+1)) - 4a^((1+1))b^((2+1)) +12ab^(3+1)# #=4a^4b + color(blue)(8a^3b^2 - 4a^2b^3) +12ab^4# #=color(blue)(4a^4b + 4a^3b^2 +12ab^4# Answer link Related questions What is Multiplication of Monomials by Polynomials? How do you multiply monomials by polynomials? How do you multiply monomials by monomials? How do you multiply #(3xy^5)(-6x^4y^2)#? How do you multiply and simplify #6ab(-10a^2 b^3+c^5)#? How do you simplify #-3a^2b(9a^2-4b^2)#? How do you multiply #y(xy^4)#? How do you multiply #(2x-1)(x^3-2x^2+3x-4)#? How do you multiply #(5n^2)(2n^5 - 2n^3 3n^7)#? How do you simplify #2t^2+(3+5)(4t)#? See all questions in Multiplication of Monomials by Polynomials Impact of this question 2304 views around the world You can reuse this answer Creative Commons License