Question
Factorize the following expressions:
$8x^2y^3- x^5$
$8x^2y^3- x^5$
✓
Answer
$8x^2y^3- x^5$
$= x^2((2y)^3 - x^3)$
$= x^2(2y - x)((2y)^2 + 2y \times x + x^2)$
$\big[\therefore$ $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$$\big]$
$= x^2(2y - x)(4y^2 + 2xy + x^2)$
$\therefore$ $8x^2y^3 - x^5 = x^2(2y - x)(4y^2 + 2xy + x^2)$
$= x^2((2y)^3 - x^3)$
$= x^2(2y - x)((2y)^2 + 2y \times x + x^2)$
$\big[\therefore$ $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$$\big]$
$= x^2(2y - x)(4y^2 + 2xy + x^2)$
$\therefore$ $8x^2y^3 - x^5 = x^2(2y - x)(4y^2 + 2xy + x^2)$
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 the sum of exterior angles of a triangle, obtained by extending its sides in the same direction is 360°.
In the adjoining figure, CE || AD and CF || BA. Prove that $\text{ar}(\triangle\text{CBG})=\text{ar}(\triangle\text{AFG}).$
→Rationalize the denominator : $\frac{12}{4 \sqrt{3}-\sqrt{2}}$
→AB, CD and EF are three concurrent lines passing throught the point O such that OF bisects $\angle\text{BOD}.$ If $\angle\text{BOF}=35^\circ,$ find $\angle\text{BOC}$ and $\angle\text{AOD}.$
→In figure, D and E are two points on BC such that BD = DE = EC. Show that $\text{ar}(\triangle\text{ABD})=\text{ar}(\triangle\text{ADE})=\text{ar}(\triangle\text{AEC}).$
→If $a+b=10$ and $a b=21$, find the value of $a^3+b^3$.
→Given three distinct points in a plane, how many lines can be drawn by joining them?
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled card board. Each cone has a base diameter of 40 cm and height 1 m . If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per $m ^2$, what will be the cost of painting all these cones? (Use $\pi=3.14$ and $\sqrt{1.04}=1.02$ )
→In the given figure, AB and CD are diameters of a circle with center O. if $\angle\text{OBD}=50^\circ,$ find $\angle\text{AOC}.$
→Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent : If the altitudes drawn on two sides of a triangle are congruent, then these two sides are congruent.