Question
Factorize:
$8a^3 - 27b^3 - 36a^2b + 54ab^2$
$8a^3 - 27b^3 - 36a^2b + 54ab^2$
✓
Answer
$8 a^3-27 b^3-36 a^2 b+54 a b^2$
$=(2 a)^3-(3 b)^3-3 \times(2 a)^2 \times 3 b+3 \times(2 a)(3 b)^2$
$=(2 a-3 b)^3\left[\because a^3-b^3-3 a^2 b+3 a b^2=(a-b)^3\right]$
$=(2 a-3 b)(2 a-3 b)(2 a-3 b)$
$\therefore 8 a^3-27 b^3-36 a^2 b+54 a b^2$
$=(2 a-3 b)(2 a-3 b)(2 a-3 b)$
$=(2 a)^3-(3 b)^3-3 \times(2 a)^2 \times 3 b+3 \times(2 a)(3 b)^2$
$=(2 a-3 b)^3\left[\because a^3-b^3-3 a^2 b+3 a b^2=(a-b)^3\right]$
$=(2 a-3 b)(2 a-3 b)(2 a-3 b)$
$\therefore 8 a^3-27 b^3-36 a^2 b+54 a b^2$
$=(2 a-3 b)(2 a-3 b)(2 a-3 b)$
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
Simplify:$\big(\sqrt{5}-\sqrt{2}\big)\big(\sqrt{2}-\sqrt{3}\big)$
→Simplify:$(1296)^\frac{1}{4}\times(1296)^\frac{1}{2}$
→In $\triangle\text{ABC, }\angle\text {A}=100^{\circ}$and $\angle\text{C}=50^{\circ}.$ Which is its shortest side?
→Prove the Theorem : A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.
Expand:
$(3x + 2)^3$
→$(3x + 2)^3$
Simplify the following expression:$(3+\sqrt{3})(5-\sqrt{2})$
→Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.
Two supplementary angles are in the ratio 4 : 5. Find the angles.
In the figure gIven below, ∆PQR is a right angled triangle. Write the names of sides opposite and adjacent to ∠P and ∠R.
A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.