Factorise:
$49 {(2 x + 3 y)}^{2} - 70 ({4 x}^{2} {- 9 y}^{2}) + 25 {(2 x - 3 y)}^{2}$

4 {(x - 9 y)}^{2}

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9 {(x + 4 y)}^{2}

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16 {(x + 9 y)}^{2}

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16 {(x - 9 y)}^{2}

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Solution

The correct option is C $16 {(x + 9 y)}^{2}$
$49 {(2 x + 3 y)}^{2} - 70 ({4 x}^{2} {- 9 y}^{2}) + 25 {(2 x - 3 y)}^{2}$
$= (7 {(2 x + 3 y))}^{2} - 2 \times 7 (2 x + 3 y) \times 5 (2 x - 3 y) + (5 {(2 x - 3 y))}^{2}$
$= {[7 (2 x + 3 y) - 5 (2 x - 3 y)]}^{2} = {[14 x + 21 y - 10 x + 15 y]}^{2}$
$= {(4 x + 36 y)}^{2} = {(4 (x + 9 y))}^{2} = 16 {(x + 9 y)}^{2}$

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Similar questions

(8 x + 3 y)^{2}

(2 x + 3 y)^{2} = 4 x^{2} + 9 y^{2} + M

Four alternative options are given for each of the following statements. Select the correct option.

The expansion of (2x − 3y)² is:

A. 2x² + 3y² + 6xy

B. 4x² + 9y² − 12xy

C. 2x² + 3y² − 6xy

D. 4x² + 9y² + 12xy

(3, 2)

16 x^{2} + 9 y^{2} - 16 x - 32 = 0

9 y^{2} - 16 x - 12 y - 57 = 0

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