Question
Factorise:
$a^3+8 b^3+64 c^3-24 a b c$
$a^3+8 b^3+64 c^3-24 a b c$
✓
Answer
$a^3+8 b^3+64 c^3-24 a b c$
$=a^3+(2 b)^3+(4 c)^3-3 \times a \times 2 b \times 4 c$
$=(a+2 b+4 c)\left[a^2+(2 b)^2+(4 c)^2-a \times 2 b-2 b \times 4 c-4 c \times a\right]$
$=(a+2 b+4 c)\left(a^2+4 b^2+16 c^2-2 a b-8 b c-4 c a\right)$
$=a^3+(2 b)^3+(4 c)^3-3 \times a \times 2 b \times 4 c$
$=(a+2 b+4 c)\left[a^2+(2 b)^2+(4 c)^2-a \times 2 b-2 b \times 4 c-4 c \times a\right]$
$=(a+2 b+4 c)\left(a^2+4 b^2+16 c^2-2 a b-8 b c-4 c a\right)$
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
Find the value of $(1296)^{0.17}\times(1296)^{0.08}.$
→In the figure gIven below, ∆PQR is a right angled triangle. Write the names of sides opposite and adjacent to ∠P and ∠R.
Evaluate the following using identities:$\big(\text{a}^2\text{b}-\text{b}^2\text{a}\big)^2$
→Evaluate:
$(103)^3$
→$(103)^3$
Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:
If $5^{3\text{x}}=125$ and $10^{\text{y}}=0.001$ find x and y.
→Retionalise the denominator of each of the following:$\frac{\sqrt2}{\sqrt5}$
→Simplify the following:
$322 \times 322-2 \times 322 \times 22+22 \times 22$
→$322 \times 322-2 \times 322 \times 22+22 \times 22$
Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when
$p ( x )=2 x ^3+7 x ^2-24 x -45, g( x )= x -3$
→$p ( x )=2 x ^3+7 x ^2-24 x -45, g( x )= x -3$
For the polynomial $mx^2 – 2x + 3$ if $p(-1) = 7$, then find m.
→