Factorise: 16x^{5} - 144x^{3}

explanation..... see, here it's 16x^{5} - 144x^{3},^{ }so in these terms, 16 and x^{3 }are common.

See this, you will understand, (**2*2*2*2*****x*x*x***x*x) - (**2*2*2*2***3*3***x*x*x**)

So the common among the two terms are **2*2*2*2*****x*x*x = 16x**^{3}

Now, when you take16x^{3 }as common, it will become like this,

16x^{3} (x^{2} - 9)

See, above this is given in the bracket (x^{2}-9), for a while, forget about **16x ^{3}**

You can also write it as (x^{2}-3^{2}), right?

So, this matches with the identity, a^{2} - b^{2} = (a+b) (a-b)

Thus, (x^{2} - 3^{2}) which will be equal to (x+3) (x-3)

So, thus the factorised number will be 16x^{3} (x+3) (x-3)

Hope, you understood....

Well, is your book is of RS Agarwal ?

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