Question

$9 {x}^{2} - 4(y + 2x) {?}^{2}$
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Answer 1

Answer:

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Answer 2

Question:

Factorise the given expression ;

9x² - 4(y+2x)².

Answer:

- (7x + 2y)•(x + 2y)

Note:

• (A+B)² = A² + 2•A•B + B²

• (A-B)² = A² - 2•A•B + B²

• A² - B² = (A+B)•(A-B)

• (A+B)² = (A-B)² + 4•A•B

• (A-B)² = (A+B)² - 4•A•B

• (A+B)³ = A³ + 3•A•B•(A+B) + B³

• (A-B)³ = A³ - 3•A•B•(A-B) + B³

• A³ + B³ = (A+B)(A² - A•B + B³)

• A³ + B³ = (A-B)(A² + A•B + B³)

• (A+B+C)² = A² + B² + C² + 2•(A•B + B•C + C•A)

Solution:

We have ;

=> 9x² - 4(y+2x)²

=> 3²•x² - 2²(y+2x)²

=> (3x)² - [2(y+2x)]²

=> [3x + 2(y+2x)]•[3x - 2(y+2x)]

=> (3x + 2y + 4x)•(3x - 2y - 4x)

=> (3x + 4x + 2y)•(3x - 4x - 2y)

=> (7x + 2y)•(-x - 2y)

=> (7x + 2y)•(-1)•(x + 2y)

=> - (7x + 2y)•(x + 2y)

Hence,

The factorised form of the given expression is ;

- (7x + 2y)•(x + 2y) .