Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$ (x+y)^4-(x-y)^4 $
$ (x+y)^4-(x-y)^4 $
✓
Answer
$ (x+y)^4-(x-y)^4 $
$ =\left[(x+y)^2\right]^2-\left[(x-y)^2\right]^2 $
$ =\left[(x+y)^2+(x-y)^2\right]\left[(x+y)^2-(x-y)^2\right] $
$ =\left(x^2+y^2+2 x y+x^2+y^2-2 x y\right)(x+y+x-y)(x+y-x+y) $
$ =\left(2 x^2+2 y^2\right)(2 x)(2 y) $
$ =2\left(x^2+y^2\right)(2 x)(2 y) $
$ =8 x y\left(x^2+y^2\right) $
$ =\left[(x+y)^2\right]^2-\left[(x-y)^2\right]^2 $
$ =\left[(x+y)^2+(x-y)^2\right]\left[(x+y)^2-(x-y)^2\right] $
$ =\left(x^2+y^2+2 x y+x^2+y^2-2 x y\right)(x+y+x-y)(x+y-x+y) $
$ =\left(2 x^2+2 y^2\right)(2 x)(2 y) $
$ =2\left(x^2+y^2\right)(2 x)(2 y) $
$ =8 x y\left(x^2+y^2\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
A crane of height 155 cm has its neck and the rest of its body in the ratio 4: 6. For your height, if your neck and the rest of the body also had this ratio, how tall would your neck be?
Write the following numbers in standard form: $0.00000083$
→A cuboid is of dimensions $60 cm \times 54 cm \times 30 cm$. How many small cubes with side 6 cm can be placed in the given cuboid?
→Draw the net of the following solid. 
(Hint: Pentagons are not congruent.)
(Hint: Pentagons are not congruent.)Find the following products:$ \left(y^2+12\right)\left(y^2+6\right) $
→What is the sum of all interior angles of a regular:
Pentagon.
Pentagon.
Find the common factors of the given term: $10pq, 20qr, 30rp$
→Find the additive inverse of the following: $\frac{-8}{-7}$
→When divided by 7 , the number 661 leaves a remainder of 3 , and 4779 leaves a remainder of 5. Without calculating, can you say what remainders the following expressions will leave when divided by 7 ? Show the solution both algebraically and visually.
(i) $4779+661$
(ii) $4779-661$
→(i) $4779+661$
(ii) $4779-661$
Convert the following ratlos to percentages.
2 : 4
2 : 4