Question

(3x + 7y)^2-(3x - 7y)^2
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Answer 1

Step-by-step explanation:

(3x+7y)2-(3x-7y)²

=9x²+49y2+42xy-[9x²+49y2-42xy]

=9x²+49y2+42xy-9x²-49y2+42xy

=42xy+42xy

=84xy

Answer 2

Step-by-step explanation:

Given:-

(3x + 7y)^2-(3x - 7y)^2

To find:-

Simplify (3x + 7y)^2-(3x - 7y)^2

Solution:-

Method-1:-

Given expression is (3x + 7y)^2-(3x - 7y)^2

It is in the form of (a+b)^2-(a-b)^2

Where a = 3x and b = 7y

We know that

(a+b)^2-(a-b)^2 = 4ab

On applying this formula to the above expression

=> 4(3x)(7y)

=> 84xy

Method -2:-

Given expression is (3x + 7y)^2-(3x - 7y)^2

(3x+7y)^2 is in the form of (a+b)^2

Where a = 3x and b = 7y

We know that

(a+b)^2 = a^2+2ab+b^2

(3x+7y)^2

=> (3x)^2+2(3x)(7y)+(7y)^2

=> 9x^2+42xy+49y^2--------(1)

and

(3x-7y)^2 is in the form of (a-b)^2

Where a = 3x and b = 7y

We know that

(a-b)^2 = a^2-2ab+b^2

(3x-7y)^2

=> (3x)^2-2(3x)(7y)+(7y)^2

=> 9x^2-42xy+49y^2-----(2)

(1)-(2)=>

(3x + 7y)^2-(3x - 7y)^2

(9x^2+42xy+49y^2)-(9x^2-42xy+49y^2)

=>9x^2+42xy+49y^2-9x^2+42xy-49y^2

=> (9x^2-9x^2)+(42xy+42xy)+(49y^2-49y^2)

=>(0)+(84xy)+(0)

=>84xy

Answer:-

The value of (3x + 7y)^2-(3x - 7y)^2 is 84xy

Used formulae:-

• (a+b)^2 = a^2+2ab+b^2

• (a-b)^2 = a^2-2ab+b^2

• (a+b)^2-(a-b)^2 = 4ab