Question
Factorize of the following expressions:
$ x^3-y^2+x-x^2 y^2 $
$ x^3-y^2+x-x^2 y^2 $
✓
Answer
$ x^3-y^2+x-x^2 y^2 $
$ =\left(x^3+x\right)-\left(x^2 y^2+y^2\right) $
$ =x\left(x^2+1\right)-y^2\left(x^2+1\right) $
$ =\left(x-y^2\right)\left(x^2+1\right)\left[\text { taking }\left(x^2+1\right) \text { as the common factor] }\right. $
$ =\left(x^3+x\right)-\left(x^2 y^2+y^2\right) $
$ =x\left(x^2+1\right)-y^2\left(x^2+1\right) $
$ =\left(x-y^2\right)\left(x^2+1\right)\left[\text { taking }\left(x^2+1\right) \text { as the common factor] }\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
Stretching Machine:
Suppose you have a stretching machine which could stretch almost anything. For example, if you put a $5$ metre stick into a $(×4)$ stretching machine (as shown below), you get a $20$ metre stick. Now if you put $10\ cm$ carrot into a $(\times 4)$ machine, how long will it be when it comes out?
→Suppose you have a stretching machine which could stretch almost anything. For example, if you put a $5$ metre stick into a $(×4)$ stretching machine (as shown below), you get a $20$ metre stick. Now if you put $10\ cm$ carrot into a $(\times 4)$ machine, how long will it be when it comes out?
Simplify: $(a^2+ 5) (b^3+ 3) + 5$
→Which of the following are perfect cube$?$
$243$
→$243$
The diameter of the base of a right circular cylinder is $42\ cm$ and its height is $10\ cm.$ Find the volume of the cylinder.
→Which of the following triplets are pythagorean$? (14, 35, 38)$
→Write the following numbers in standard form: $0.00000165$
→Use isometric dot paper to draw each figure.A rectangular prism with length $4$ units, width $2$ units and height $2$ units.
→$\frac{1}{6}$ of the class students are above average, $\frac{1}{4}$ are average and rest are below average. If there are $48$ students in all, how many students are below average in the class?
→Factorize of the following algebraic expression: $4(x + y)(3a - b) + 6(x + y)(2b - 3a)$
→The cost of $27\ kg$ of iron is $Rs\ 1,080$, what will be the cost of $120\ kg$ of iron of the same quality?
→