Factorise :
(1−a2)(1−b2)+4ab(1 - a^2)(1 - b^2) + 4ab(1−a2)(1−b2)+4ab
3 Likes
(1−a2)(1−b2)+4ab=1(1−b2)−a2(1−b2)+4ab=1−b2−a2+a2b2+4ab=1−b2−a2+a2b2+2ab+2ab=(1+a2b2+2ab)−(b2+a2−2ab)=(1+ab)2−(a−b)2=((1+ab)−(a−b))((1+ab)+(a−b))=(1+ab−a+b)(1+ab+a−b)(1 - a^2)(1 - b^2) + 4ab\\[1em] = 1(1 - b^2) - a^2(1 - b^2) + 4ab\\[1em] = 1 - b^2 - a^2 + a^2b^2 + 4ab\\[1em] = 1 - b^2 - a^2 + a^2b^2 + 2ab + 2ab\\[1em] = (1 + a^2b^2 + 2ab) - (b^2 + a^2 - 2ab)\\[1em] = (1 + ab)^2 - (a - b)^2\\[1em] = \Big((1 + ab) - (a - b)\Big)\Big((1 + ab) + (a - b)\Big)\\[1em] = (1 + ab - a + b)(1 + ab + a - b)\\[1em](1−a2)(1−b2)+4ab=1(1−b2)−a2(1−b2)+4ab=1−b2−a2+a2b2+4ab=1−b2−a2+a2b2+2ab+2ab=(1+a2b2+2ab)−(b2+a2−2ab)=(1+ab)2−(a−b)2=((1+ab)−(a−b))((1+ab)+(a−b))=(1+ab−a+b)(1+ab+a−b)
Hence, (1−a2)(1−b2)+4ab=(1+ab−a+b)(1+ab+a−b)(1 - a^2)(1 - b^2) + 4ab = (1 + ab - a + b)(1 + ab + a - b)(1−a2)(1−b2)+4ab=(1+ab−a+b)(1+ab+a−b).
Answered By
32a4−8a232a^4 - 8a^232a4−8a2
2(ab+cd)−a2−b2+c2+d22(ab + cd) - a^2 - b^2 + c^2 + d^22(ab+cd)−a2−b2+c2+d2
(x2+y2−z2)2−4x2y2(x^2 + y^2 - z^2)^2 - 4x^2y^2(x2+y2−z2)2−4x2y2
8(3x−2y)2−6x+4y−18(3x - 2y)^2 - 6x + 4y - 18(3x−2y)2−6x+4y−1
