Question

add the following algebraic expression:a^2b[b+c]+b^2c[b-c]and c^2b[b-c]-bc[a^2+b^2].​

Answer 1

Answer :

$\left(ab\right)^{2}-bc^{3} \\ or \\ b\left(ba^{2}-c^{3}\right)$

Step by Step :

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

hope it helped!