Simplify (2 x-5 y)^3-(2 x+5 y)^3. - Vidyadip

Question

Simplify $(2 x-5 y)^3-(2 x+5 y)^3$.

✓

Answer

$\left.(2 x-5 y)^3-(2 x+5 y)^3=\{(2 x-5 y)-(2 x+5 y)\}(2 x-5 y)^2+(2 x-5 y)(2 x+5 y)+(2 x+5 y)^2\right\}$
${\left[\therefore a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right]}$
$=(2 x-5 y-2 x-5 y)\left(4 x^2+25 y^2-20 x y+4 x^2-25 y^2+4 x^2+25 y^2+20 x y\right)$
$=(-10 y)\left(2 x^2+25 y^2\right)$
$=-120 x^2 y-250 y^3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Polynomials→Polynomials — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Simplify: $\frac{2}{\sqrt5+\sqrt3}+\frac{1}{\sqrt3+\sqrt2}-\frac{3}{\sqrt5+\sqrt2}$

If $a+b+c=0$ and $a^2+b^2+c^2=16$, find the value of $a b+b c+c a$.

It being given that $\sqrt{3}=1.732,\sqrt{5}=2.236,\sqrt{6}=2.449$ and $\sqrt{10}=3.162,$ find to three places of decimal, the value of the following: $\frac{1+2\sqrt{3}}{2-\sqrt{3}}$

A circus tent is cylindrical to a height of $3$ metres and conical above it. If its diameter is $105m$ and the slant height of the conical portion is $53m,$ calculate the length of the canvas 5m wide to make the required tent. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$

Define supplementary angles.

Determine which of the following polynomials has $x - 2$ a factor:
$i. 3x^2 + 6x - 24$
$ii. 4x^2+ x – 2$

It being given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{10}=3.162,$ find the value of three places of decimals, of the following: $\frac{2-\sqrt{3}}{\sqrt{3}}$

Represent $\sqrt{9.3}$ on the number line.

A sphere of diameter $15.6\ cm$ is melted and cast into a right circular cone of height $31.2\ cm$. Find the diameter of the base of the cone.

A metal cube of edge $12\ cm$ is melted and formed into three smaller cubes. If the edges of the two smaller cubes are $6\ cm$ and $8\ cm$, find the edge of the third smaller cube.