What is factor 16x^4+9y^4+24x^2*y^2 ?

The solution to factor 16x^4+9y^4+24x^2*y^2 is (4x^2+3y^2)^2

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factor 16x^4+9y^4+24x^2*y^2

factor

16 x^{4} + 9 y^{4} + 24 x^{2} \cdot y^{2}

(4 x^{2} + 3 y^{2})^{2}

Solution steps

16 x^{4} + 9 y^{4} + 24 x^{2} y^{2}

Group by common factors

= 16 x^{4} + 24 x^{2} y^{2} + 9 y^{4}

Break the expression into groups

= (16 x^{4} + 12 x^{2} y^{2}) + (12 x^{2} y^{2} + 9 y^{4})

Factor out

4 x^{2}

from

16 x^{4} + 12 x^{2} y^{2} : 4 x^{2} (4 x^{2} + 3 y^{2})

Factor out

3 y^{2}

from

12 x^{2} y^{2} + 9 y^{4} : 3 y^{2} (4 x^{2} + 3 y^{2})

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

Factor out common term

4 x^{2} + 3 y^{2}

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

Apply exponent rule:

aa = a^{2}

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

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

(2 a + 3) (3 a + 2 b)

x 3 y^{23}

a (- 2.3) b (5.4) c (2 - 6)

(15 x^{2} - 2 x + 10) + (13 x + 15)

343 x^{3} y + 512 y^{4}

What is factor 16x^4+9y^4+24x^2*y^2 ?
The solution to factor 16x^4+9y^4+24x^2*y^2 is (4x^2+3y^2)^2