What is expand (15+x)((15+x)/2)^2 ?

The solution to expand (15+x)((15+x)/2)^2 is (x^3+45x^2+675x+3375)/4

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expand (15+x)((15+x)/2)^2

expand

(15 + x) (\frac{15 + x}{2})^{2}

\frac{x ^{3} + 45 x ^{2} + 675 x + 3375}{4}

Solution steps

(15 + x) (\frac{15 + x}{2})^{2}

= (\frac{15 + x}{2})^{2} (15 + x)

Apply the distributive law:

a (b + c) = ab + a c

(\frac{15 + x}{2})^{2} (15 + x) = (\frac{15 + x}{2})^{2} \cdot 15 + (\frac{15 + x}{2})^{2} x

= (\frac{15 + x}{2})^{2} \cdot 15 + (\frac{15 + x}{2})^{2} x

Simplify

(\frac{15 + x}{2})^{2} \cdot 15 + (\frac{15 + x}{2})^{2} x : \frac{x ^{3} + 45 x ^{2} + 675 x + 3375}{4}

= \frac{x ^{3} + 45 x ^{2} + 675 x + 3375}{4}

+ 10 y^{2} a t (2, 1, - 14)

\frac{4 x ^{2} + 16 x}{( x - 2 ) ^{2} ( x ^{2} + 4 )}

(\frac{1}{4} - x) (\frac{1}{4} + x)

80 (10 + 1)

2 (- 5 + 5)

What is expand (15+x)((15+x)/2)^2 ?
The solution to expand (15+x)((15+x)/2)^2 is (x^3+45x^2+675x+3375)/4