4a^2+12ab+9b^2-8a-12b
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.(2a)^2+2×2a×3b+(3b)^2-4(2a+3b)
.(2a+3b)^2-4(2a+3b)=(2a+3b)(2a+3b-4)
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Step-by-step explanation:
The given equation is:
4a^{2}+12ab+9b^{2}-8a-12b4a
2
+12ab+9b
2
−8a−12b
Rewriting the terms and taking 12ab as 6ab+6ab, we get
4a^{2}-8a+6ab+6ab+9b^{2}-12b4a
2
−8a+6ab+6ab+9b
2
−12b
Taking 2a common from first three terms and 3b common from last three terms of the above equation,
2a(2a-4+3b)+3b(2a+3b-4)2a(2a−4+3b)+3b(2a+3b−4)
(2a+3b)(2a-4+3b)(2a+3b)(2a−4+3b) which is the required solution.
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