Question

Find the product:
$(a-2b+3c)(a{b}^2-a^{2}b)$=$3a^2{b}^2-a^{3}b-2a{b}^3-3a^{2}bc+30b^{2}c$

• A. True
• B. False

Answer 1

The correct option is B False

We multiply the given expressions $(a-2b+3c)$ and $(a{b}^2-a^{2}b)$ as shown below:

$(a-2b+3c)(a{b}^2-a^{2}b)=a(a{b}^2-a^{2}b)-2b(a{b}^2-a^{2}b)+3c(a{b}^2-a^{2}b)=a^2{b}^2-a^{3}b-2a{b}^3+2a^2{b}^2+3a{b}^{2}c-3a^{2}bc=(a^2{b}^2+2a^2{b}^2)-a^{3}b-2a{b}^3-3a^{2}bc+3a{b}^{2}c\left(Combiningliketerms\right)=a^2{b}^2(1+2)-a^{3}b-2a{b}^3-3a^{2}bc+3a{b}^{2}c=3a^2{b}^2-a^{3}b-2a{b}^3-3a^{2}bc+3a{b}^{2}c$

Hence, $(a-2b+3c)(a{b}^2-a^{2}b)=3a^2{b}^2-a^{3}b-2a{b}^3-3a^{2}bc+3a{b}^{2}c$.