Question

Find the product of the following (2x+3) (2x-6)

Answer 1

Answer:

(2x + 2x) (3-6)

(4x) (-3)

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Answer 2

(2x + 3)(2x - 6) = 4x² - 6x - 18

Given :

The expression (2x + 3)(2x - 6)

To find :

The product using suitable identity

Formula :

We are aware of the identity that

$\displaystyle \sf{(y + a)(y + b) = {y}^{2} + (a + b)y + ab }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(2x + 3)(2x - 6)

Step 2 of 2 :

Simplify the given expression

We are aware of identity that

$\displaystyle \sf{(y + a)(y + b) = {y}^{2} + (a + b)y + ab }$

We take y = 2x , a = 3 , b = - 6

Thus we get

$\displaystyle \sf{ (2x + 3)(2x - 6) }$

$\displaystyle \sf{ = {(2x)}^{2} + (3 - 6)(2x) + (3 \times - 6)}$

$\displaystyle \sf{ = 4{x}^{2} + (-3 \times 2x) -18}$

$\displaystyle \sf{ = 4{x}^{2} - 6x - 18}$

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