What is factor 4a^4+12a^2b+9b^2 ?

The solution to factor 4a^4+12a^2b+9b^2 is (2a^2+3b)^2

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factor 4a^4+12a^2b+9b^2

factor

4 a^{4} + 12 a^{2} b + 9 b^{2}

(2 a^{2} + 3 b)^{2}

Solution steps

4 a^{4} + 12 a^{2} b + 9 b^{2}

Break the expression into groups

= (4 a^{4} + 6 a^{2} b) + (6 a^{2} b + 9 b^{2})

Factor out

2 a^{2}

from

4 a^{4} + 6 a^{2} b : 2 a^{2} (2 a^{2} + 3 b)

Factor out

3 b

from

6 a^{2} b + 9 b^{2} : 3 b (2 a^{2} + 3 b)

= 2 a^{2} (2 a^{2} + 3 b) + 3 b (2 a^{2} + 3 b)

Factor out common term

2 a^{2} + 3 b

= (2 a^{2} + 3 b) (2 a^{2} + 3 b)

Apply exponent rule:

aa = a^{2}

(2 a^{2} + 3 b) (2 a^{2} + 3 b) = (2 a^{2} + 3 b)^{2}

= (2 a^{2} + 3 b)^{2}

\frac{t}{t ^{2}}

ln ((e^{u} + 3) - 3)

7 (h + 3 k)

y + x^{4} y^{5}

- 15 + (- 5)

What is factor 4a^4+12a^2b+9b^2 ?
The solution to factor 4a^4+12a^2b+9b^2 is (2a^2+3b)^2