What is factor 3/4 (n+1)^2-2 ?

The solution to factor 3/4 (n+1)^2-2 is ((sqrt(3)(n+1))/2+sqrt(2))((sqrt(3)(n+1))/2-sqrt(2))

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factor 3/4 (n+1)^2-2

factor

\frac{3}{4} (n + 1)^{2} - 2

(\frac{3 ( n + 1 )}{2} + 2) (\frac{3 ( n + 1 )}{2} - 2)

Solution steps

\frac{3}{4} (n + 1)^{2} - 2

Rewrite

\frac{3 ( n + 1 ) ^{2}}{4} - 2

(\frac{3}{4} (n + 1))^{2} - (2)^{2}

= (\frac{3}{4} (n + 1))^{2} - (2)^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(\frac{3}{4} (n + 1))^{2} - (2)^{2} = (\frac{3}{4} (n + 1) + 2) (\frac{3}{4} (n + 1) - 2)

= (\frac{3}{4} (n + 1) + 2) (\frac{3}{4} (n + 1) - 2)

Refine

= (\frac{3 ( n + 1 )}{2} + 2) (\frac{3 ( n + 1 )}{2} - 2)

2 a c - 2 a d + b c - b d

87.5 \cdot 480000

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

4 - d 4 e 2

7 a - 7 b + ma - mb

What is factor 3/4 (n+1)^2-2 ?
The solution to factor 3/4 (n+1)^2-2 is ((sqrt(3)(n+1))/2+sqrt(2))((sqrt(3)(n+1))/2-sqrt(2))