What is factor 25n^2+40np+16p^2 ?

The solution to factor 25n^2+40np+16p^2 is (4p+5n)^2

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factor 25n^2+40np+16p^2

factor

25 n^{2} + 40 n p + 16 p^{2}

(4 p + 5 n)^{2}

Solution steps

25 n^{2} + 40 n p + 16 p^{2}

Group by common factors

= 16 p^{2} + 40 p n + 25 n^{2}

Rewrite in the form of

a^{2} + 2 ab + b^{2} :

16 p^{2} = (4 p)^{2}

25 n^{2} = (5 n)^{2}

40 p n = 2 \cdot 4 p \cdot 5 n

= (4 p)^{2} + 2 \cdot 4 p \cdot 5 n + (5 n)^{2}

Apply Perfect Square Formula:

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

(4 p)^{2} + 2 \cdot 4 p \cdot 5 n + (5 n)^{2} = (4 p + 5 n)^{2}

= (4 p + 5 n)^{2}

x - \frac{x + 1}{4} = \frac{2 x}{5} + \frac{3}{2}

2 x^{2} - 8 x + 2 = 0

- 6 x > 24

\frac{2}{3} + \frac{2}{3} + \frac{1}{4} - \frac{1}{3}

4 - 3 (1 - x) \leq 1

What is factor 25n^2+40np+16p^2 ?
The solution to factor 25n^2+40np+16p^2 is (4p+5n)^2