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Definition of Function

Expand the fo...

Question

Expand the following:

$(v) (2 x - 5) (2 x + 5) (2 x - 3)$

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Solution

Given: Expression is $(2 x - 5) (2 x + 5) (2 x - 3)$ .

First expand the given binomials $(2 x - 5) (2 x + 5)$ by the difference of square identity.

$\Rightarrow (2 x - 5) (2 x + 5) = (2 x)^{2} - (5)^{2}$

$[∵ (a + b) (a - b) = a^{2} - b^{2}]$

$= 4 x^{2} - 25$

Now, multiply the result $(4 x^{2} - 25)$ by $(2 x - 3)$

$\Rightarrow (4 x^{2} - 25) (2 x - 3) = 4 x^{2} \times (2 x - 3) - 25 \times (2 x - 3)$

$= 8 x^{3} - 12 x^{2} - 50 x + 75$

Hence, $(2 x - 5) (2 x + 5) (2 x - 3) = 8 x^{3} - 12 x^{2} - 50 x + 75$ .

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Definition of Function

Standard XII Mathematics

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