Question

12. The product of (2x+3y)(2x-3y) is:​

Answer 1

GIVEN :

(2x+3y)(2x-3y)

TO FIND :

Product of given expression.

FORMULA USED:

(a+b) (a-b) = a²-b²

SOLUTION :

✬ To find the product of (2x+3y)(2x-3y) we will use the formula :- (a+b) (a-b) = a²-b²

➮(2x+3y)(2x-3y)

➮ (2x)²-(3y)²

➮ 4x² - 9y²

ANSWER : 4x² - 9y²

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⚫ LEARN MORE :-

1. (a+b)²=a²+b²+2ab
2. (a-b)²=a²+b²-2ab

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Answer 2

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The given expression (2x+3y)(2x−3y) can be expanded as shown below:

(2x+3y)(2x−3y)

=[(2x×2x)+(2x×−3y)+(3y×2x)+(3y×−3y)]

=4x² −6xy+6xy−9y²

=4x² −9y²

Hence (2x+3y)(2x−3y)=4x² −9y²

$\huge\boxed{\fcolorbox{black}{pink}{Other Important Identities}}$

Some Standard Algebraic Identities list are given below:

Identity I:-

• (a + b)2 = a2 + 2ab + b2

Identity II:

• (a – b)2 = a2 – 2ab + b2

Identity III:-

• a2 – b2= (a + b)(a – b)

Identity IV:-

• (x + a)(x + b) = x2 + (a + b) x + ab.

Identity V:-

• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.

Identity VI:-

• (a + b)3 = a3 + b3 + 3ab (a + b)

Identity VII:-

• (a – b)3 = a3 – b3 – 3ab (a – b)

Identity VIII:-

• a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)