Question
Find the following product:
$\left(x^3-y^3\right)\left(x^2+y^2\right)$
$\left(x^3-y^3\right)\left(x^2+y^2\right)$
✓
Answer
$\left(x^3-y^3\right)\left(x^2+y^2\right)$
$=x^3\left(x^2+y^2\right)-y^3\left(x^2+y^2\right)$
$=\left(x^3 \times x^2+x^3 \times y^2\right)-\left(y^3 \times x^2+y^3 \times y^2\right)$
$=x^5+x^3 y^2-x^2 y^3-y^5$
$=x^3\left(x^2+y^2\right)-y^3\left(x^2+y^2\right)$
$=\left(x^3 \times x^2+x^3 \times y^2\right)-\left(y^3 \times x^2+y^3 \times y^2\right)$
$=x^5+x^3 y^2-x^2 y^3-y^5$
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