Question

How do you multiply (2x+3)(2x−3)?

Answer 1

Answer: $4x {}^{2} - 9$

Step by step explanation :

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

Use the distributive property. Multiply the second parenthesis by each term from the first parenthesis.

$= > 2x \: \times (2x - 3) + 3(2x - 3)$

Remove parenthesis. Distribute 2x through the parenthesis.

$= > 4x {}^{2} - 6x + 3(2x - 3)$

Distribute 3 through the parenthesis.

$= > 4x {}^{2} - 6x + 6x - 9$

Eliminate the opposites.

$= > 4x {}^{2} - 9$

Answer 2

Using the identity,

(a + b)(a - b) = a² - b²

1.  Taking  a = 2x  &  b = 3,

⇒  (a + b)(a - b) = a² - b²

⇒  (2x + 3)(2x - 3) = (2x)² - (3)²

⇒  (2x + 3)(2x - 3) = 4x² - 9

2.  Taking  a = 2x  &  b = -3,

⇒  (a + b)(a - b) = a² - b²

⇒  (2x - 3)(2x + 3) = (2x)² - (-3)²

⇒  (2x - 3)(2x + 3) = 4x² - 9

Hence the product is 4x² - 9.