What is factor 16+40x+25x^2 ?

The solution to factor 16+40x+25x^2 is (5x+4)^2

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factor 16+40x+25x^2

factor

16 + 40 x + 25 x^{2}

(5 x + 4)^{2}

Solution steps

16 + 40 x + 25 x^{2}

Write in the standard form

= 25 x^{2} + 40 x + 16

Rewrite in the form of

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

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

16 = 4^{2}

40 x = 2 \cdot 5 x \cdot 4

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

Apply Perfect Square Formula:

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

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

= (5 x + 4)^{2}

4 x^{2} + 17 x + 14 = 0

- 3 + 3 x^{5}

5 x = 3 x - 10 + 2 x

- 2 y = - 8

\frac{1}{4} (8 x + 16) = 4 x