Factorize the following
1).$ 66(y^4-5y^3-24y^2) +6y(y-8)$
2).$ 36mn(25m^2- 49n^2)+ 4mn(5m + 7n)$
3). $x(x+2)(x+4)(x+6) + x(x+ 2)$

Solution:

1). $66(y^{4} -5y^{3}-24y^{2}) +6y(y-8)$

= $66y^{2}(y^{2} -5y-24) +6y(y-8)$

= $66y^{2}(y-8)(y + 3) + 6y(y -8)$

= $6y(y-8)[11y(y+3) + 1]$

= $6y(y - 8)(11y^{2} + 33y + 1)$

2) $36mn(25m^{2} - 49n^{2})+ 4mn(5m + 7n)$

= $36mn(5m + 7n)(5m - 7n)+ 4mn(5m + 7n)$

= $4mn(5m + 7n)[9(5m - 7) + 1]$

= $4mn(5m + 7n)(45m-62)$ 

3)$x(x+2)(x+4)(x+6) + x(x+ 2)$

= $x(x+2)[(x+4)(x+6) + 1]$

= $x(x+2)(x^{2} + 10x + 25)$ 

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Updated on: 10-Oct-2022

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