#### (i) x^{2} + x^{5}

Take out common in all terms we get,

x^{2}(1 + x^{3})

x^{2}(1^{3} + x^{3})

We know that, a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2})

Where, a = 1, b = x

= x^{2} [(1 + x) (1^{2} – (1 × x) + x^{2})]

= x^{2} (1 + x) (1 – x + x^{2})

##### (ii)32x^{4} – 500x

Take out common in all terms we get,

4x(8x^{3} – 125)

Above terms can be written as,

4x((2x)^{3} – 5^{3})

We know that, a^{3} – b^{3} = (a – b) (a^{2} + ab + b^{2})

Where, a = 2x, b = 5

= 4x(2x – 5) ((2x)^{2} + (2x × 5) + 5^{2})

= 4x(2x – 5) (4x^{2} + 10x + 25)

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