Question

factorise: (1+x)^2 (1+y^2) - (1+y)^2 (1+x^2)​

Answer 1

Answer:

(1+x)²(1+y²)-(1+y)²(1+x²)

let's solve it in parts so-:

(1+x)²

1²+2(1x)+x²

=>1+2x+x²

(1+y)²

1²+2(1y)+y²

=>1+2y+y²

so now we have,

(1+2x+x²)(1+y²)-(1+2y+y²)(1+x²)

(1×1+1×2x+1×x²)+(y²×1+y²×2x+y²×x²)

(1+2x+x²)+(y²+2xy²+x²y²)

(1+2y+y²)(1+x²)

=> (1×1+1×2y+1×y²)+(x²×1+x²×2y+x²×y²)

(1+2y+y²)+(x²+2x²y+x²y²)

now we have,

(1+2x+x²)+(y²+2xy²+x²y²)-(1+2y+y²)+(x²+2x²y+x²y²)

collect like terms,

1-1+x²y²-x²y²+x²-x²+y²-y²=0

so the numbers left are-:

2x+2xy²+2y+2x²y=> ans