Question
Factorise:$\frac{\text{x}^3}{216}-8\text{y}^3$
✓
Answer
$\frac{\text{x}^3}{216}-8\text{y}^3$$=\Big(\frac{\text{x}}{6}\Big)^3-(2\text{y})^3$
$=\Big(\frac{\text{x}}{6}-2\text{y}\Big)\bigg[\Big(\frac{\text{x}}{6}\Big)^2+\Big(\frac{\text{x}}{6}\Big)(2\text{y})+(2\text{y})^2\bigg]$
$=\Big(\frac{\text{x}}{6}-2\text{y}\Big)\Big(\frac{\text{x}^2}{36}+\frac{\text{xy}}{3}+4\text{y}^2\Big)$
$=\Big(\frac{\text{x}}{6}-2\text{y}\Big)\bigg[\Big(\frac{\text{x}}{6}\Big)^2+\Big(\frac{\text{x}}{6}\Big)(2\text{y})+(2\text{y})^2\bigg]$
$=\Big(\frac{\text{x}}{6}-2\text{y}\Big)\Big(\frac{\text{x}^2}{36}+\frac{\text{xy}}{3}+4\text{y}^2\Big)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Multiply : $(3 \sqrt{2}-\sqrt{3})(4 \sqrt{3}-\sqrt{2})$
→Factorise:
$1-27 a^3$
→$1-27 a^3$
Examine whether the following number are rational or irrational:$\frac{2\sqrt{13}}{3\sqrt{52}-4\sqrt{117}}$
→Points D and E are the midpoints of side AB and side AC of ∆ABC respectively. Point F is on ray ED such that ED = DF. Prove that □AFBE is a parallelogram. For this example write ‘given’ and ‘to prove’ and complete the proof.
Given: D and E are the midpoints of side AB and side AC respectively.
ED = DF
To prove: □AFBE is a parallelogram.
In the following, use factor theorem to find whether polynomial $g(x)$ is a factor of polynomial $f(x)$ or, not:
$f(x)=x^5+3 x^4-x^3-3 x^2+5 x+15, g(x)=x+3$
→$f(x)=x^5+3 x^4-x^3-3 x^2+5 x+15, g(x)=x+3$
Rationalise the denominator of the following:$\frac{1}{5+3\sqrt{2}}$
→Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when
$p(x)=x^4-x^2-12, g(x)=x+2$
→$p(x)=x^4-x^2-12, g(x)=x+2$
A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
To verify the different properties of quadrilaterals.
Evaluate the following using identities:$(2\text{x} +\text{y})(2\text{x} - \text{y})$
→