# Find the Value of a²+b² is

If 4x^{2}+12xy-8x+9y^{2}-12y = (ax+by)(ax+by-4). Then the value of a²+b² is:

- 13
- 25
- 5
- 10

**Answer: (1) 13**

**Explanation:-
**

4x^{2} + 12xy – 8x + 9y^{2}– 12y = (ax + by) (ax + by – 4)

(2x)^{2} + 2 x 2X x 3y – 8x + (3y)^{2} – 12y = (ax + by) (ax + by – 4)

(2x + 3y)^{2} – 4(2x + 3y) = (ax + by) (ax + by – 4)

(2x + 3y) (2x + 3y – 4) = (ax + by) (ax + by – 4)

Comparing on both side,

Then, a = 2 & b = 3

The value of a^{2} + b^{2} = 2^{2} + 3^{2}

= 2 x 2 + 3 x 3

= 4 + 9

= 13

Hence, the answer is (1) 13.

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