Question

Simplify: $(x^3+y^3)(x^2+xy+y^2)$

• A. $x^5+x^{4}y+x^3{y}^2+x{y}^3+x{y}^4+y^5$
• B. $x^5+x^{4}y+y^6+x^2{y}^3+x{y}^4+y^5$
• C. $x^5+x^{4}y+x^3{y}^2+x^2{y}^3+x{y}^4+y^5$
• D. $x^9+x^{4}y+x^3{y}^2+x^2{y}^3+x{y}^4+y^9$

Answer 1

The correct option is C $x^5+x^{4}y+x^3{y}^2+x^2{y}^3+x{y}^4+y^5$

$(x^3+y^3)(x^2+xy+y^2)$
First, multiply each term of the trinomial by the first term of the binomial. Then multiply each term of the trinomial by the second term of the binomial.
$=$ $x^3.x^2+x^3.xy+x^3.y^2+y^3.x^2+y^3.xy+y^3.y^2$
$=$ $x^5+x^{4}y+x^3{y}^2+x^2{y}^3+x{y}^4+y^5$