Question
Factorize:
$64a^3 + 125b^3 + 240a^2b + 300ab^2$
$64a^3 + 125b^3 + 240a^2b + 300ab^2$
✓
Answer
$64 a^3+125 b^3+240 a^2 b+300 a b^2$
$=(4 a)^3+(5 b)^3+3 \times(4 a)^2 \times 5 b+3(4 a)(5 b)^2$
$=(4 a+5 b)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(4 a+5 b)(4 a+5 b)(4 a+5 b)$
$\therefore 64 a^3+125 b^3+240 a^2 b+300 a b^2$
$=(4 a+5 b)(4 a+5 b)(4 a+5 b)$
$=(4 a)^3+(5 b)^3+3 \times(4 a)^2 \times 5 b+3(4 a)(5 b)^2$
$=(4 a+5 b)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(4 a+5 b)(4 a+5 b)(4 a+5 b)$
$\therefore 64 a^3+125 b^3+240 a^2 b+300 a b^2$
$=(4 a+5 b)(4 a+5 b)(4 a+5 b)$
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
Prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also.
Given: line AB || line CD and line EF intersects them at P and Q respectively.
line EF ⊥ line AB
To prove: line EF ⊥ line CD
How many planes can be made to pass through three distinct points?
Sin θ =$\frac{1}{2}$.Find Cos θ= , Tan θ= ?
→How many planes can be made to pass through a line and a point not on the line?
Examine whether the following numbers are rational or irrational.$\sqrt{\frac{13}{117}}$
→Write the ratio of first quantity to second quantity in the reduced form : 1.5 kg, 2500 gm
Factorise:
$x^2-y^2+6 y-9$
→$x^2-y^2+6 y-9$
Factorise:
$x(x+y)^3-3 x^2 y(x+y)$
→$x(x+y)^3-3 x^2 y(x+y)$
Find the value to three place of decimals of each of the following. It is given that $\sqrt2=1.414,\ \sqrt3=1.732,\ \sqrt5=2.236,\ \sqrt10=3.162.$$\frac{2+\sqrt{3}}{3}$
→Simplify the following:$\frac{5\times25^{\text{n}+1}-25\times5^{2\text{n}}}{5\times5^{2\text{n}+3}-(25)^{\text{n}+1}}$
→