Question
Using the standard formulae, expand:
$(5 x-3 y)^2$
$(5 x-3 y)^2$
✓
Answer
$25 x^2+9 y^2-30 x y$
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→Factorise:
$(a+b)^3+(a-b)^3$
$\begin{aligned} \text { [Hint. Given Exp. } & =x^3+y^3 \text {, where }(a+b)=x \text { and }(a-b)=y \\ & =(x+y)\left[x^2-x y+y^2\right] \\ & =(a+b+a-b)\left[(a+b)^2-\left(a^2-b^2\right)+(a-b)^2\right] \\ & \left.=2 a\left(a^2+3 b^2\right)\right]\end{aligned}$
→$(a+b)^3+(a-b)^3$
$\begin{aligned} \text { [Hint. Given Exp. } & =x^3+y^3 \text {, where }(a+b)=x \text { and }(a-b)=y \\ & =(x+y)\left[x^2-x y+y^2\right] \\ & =(a+b+a-b)\left[(a+b)^2-\left(a^2-b^2\right)+(a-b)^2\right] \\ & \left.=2 a\left(a^2+3 b^2\right)\right]\end{aligned}$
Write down the values of:
$(3+2 \sqrt{5})^2$
→$(3+2 \sqrt{5})^2$