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151.

`32x^4-500x`

Answer» Correct Answer - `4x(2x-5)(4x^2+10x+25)`
`32x^4-500x=4x(8x^3-125)`.
Discussion
152.

Factorise `(i) 27-125a^3-135a+225a^2` `(ii) 1-64a^3-12a +48a^2`.

Answer» We have
`(i) 27-125a^3-135a+225a^2`
`=3^3-(5a)^3-45(3-5a)`
`=3^3-(5a)^3-(3xx3xx5a)(3-5a)`.
`=(3-5a)^3=(3-5a)(3-5a)(3-5a)`.
Discussion
153.

factorise `2x^2 +y^2 +8z^2-2sqrt(2)xy+4sqrt(2)yz-8xz`

Answer» We observe here that `2sqrt(2)xy and -8zx` are negative terms in the given expression and x occurs in both the terms.
So, we wire ` 2x^2 " as " (-sqrt(2x))^2`.
`therefore 2x^2+y^2+8z^2-2sqrt(2)xy+4sqrt(2)yz-8zx`
`=(-sqrt(2x))^2+y^2(2sqrt(2)z)^2+{2xx(-sqrt(2)x)xxy}+{2xxy xx (2sqrt(2)z)}+{2xx(2sqrt(2)z)xx(-sqrt(2)x)}`
`=(-sqrt(2)x+y+2sqrt(2)z)^2`.
Discussion