Q2 R of 52 Page 127

Let’s resolve into factors

x6y6-9x3y3 + 8


(x3y3)2-9x3y3 + 8 … (1)

To resolve it into factors we first resolve 8


8=2×2×2


Given, x2 + (m + n)x + mn=(x + m)(x + n) … (2)


Comparing 1 and 2


m + n =-9


mn =8


∴ (1) can be written as


(x3y3)2-8x3y3-x3y3 + 8


= (x3y3-8)( x3y3-1)


Apply the formula a3 - b3 = (a - b)(a2 + ab + b2) in (x3y3-8) and ( x3y3-1) as:


(x3y3-8) = ((xy)3 – 23)


= (xy-2) (x2y2 + 4 + 2xy)


(x3y3-1) = ((xy)3 – 13)


= (xy-1) (x2y2 + 1 + xy)


So,


(x3y3)2-8x3y3-x3y3 + 8 = (xy-2) (x2y2 + 4 + 2xy) (xy-1) (x2y2 + 1 + xy)


∴ the resolved factors are (xy-2) (x2y2 + 4 + 2xy) (xy-1) (x2y2 + 1 + xy)


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