What is factor 25(n-6)^2+70(n-6)+49 ?

The solution to factor 25(n-6)^2+70(n-6)+49 is (5n-23)^2

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factor 25(n-6)^2+70(n-6)+49

factor

25 (n - 6)^{2} + 70 (n - 6) + 49

(5 n - 23)^{2}

Solution steps

25 (n - 6)^{2} + 70 (n - 6) + 49

Rewrite

25 (n - 6)^{2} + 70 (n - 6) + 49

(5 (n - 6))^{2} + 2 \cdot 5 (n - 6) \cdot 7 + 7^{2}

= (5 (n - 6))^{2} + 2 \cdot 5 (n - 6) \cdot 7 + 7^{2}

Apply Perfect Square Formula:

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

a = 5 (n - 6), b = 7

= (5 (n - 6) + 7)^{2}

Expand

5 (n - 6) + 7 : 5 n - 23

= (5 n - 23)^{2}

12 - (\frac{5 - 1}{2})

(2 x^{2}) + (3 x + 1)

25 + (- x)

u + 4 t + ux + 4 t x

49 x^{2} + 63 + 8

What is factor 25(n-6)^2+70(n-6)+49 ?
The solution to factor 25(n-6)^2+70(n-6)+49 is (5n-23)^2