What is expand np*(np-p+1)^2 ?

The solution to expand np*(np-p+1)^2 is n^3p^3-2n^2p^3+2n^2p^2+np^3-2np^2+np

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expand np*(np-p+1)^2

expand

n p \cdot (n p - p + 1)^{2}

n^{3} p^{3} - 2 n^{2} p^{3} + 2 n^{2} p^{2} + n p^{3} - 2 n p^{2} + n p

Solution steps

n p (n p - p + 1)^{2}

(n p - p + 1)^{2} = n^{2} p^{2} - 2 n p^{2} + 2 n p + p^{2} - 2 p + 1

= n p (n^{2} p^{2} + p^{2} - 2 n p^{2} + 2 n p - 2 p + 1)

Distribute parentheses

= n p n^{2} p^{2} + n p (- 2 n p^{2}) + n p \cdot 2 n p + n p p^{2} + n p (- 2 p) + n p \cdot 1

Apply minus-plus rules

+ (- a) = - a

= n^{2} n p^{2} p - 2 nn p^{2} p + 2 nn pp + n p^{2} p - 2 n pp + 1 \cdot n p

Simplify

n^{2} n p^{2} p - 2 nn p^{2} p + 2 nn pp + n p^{2} p - 2 n pp + 1 \cdot n p : n^{3} p^{3} - 2 n^{2} p^{3} + 2 n^{2} p^{2} + n p^{3} - 2 n p^{2} + n p

= n^{3} p^{3} - 2 n^{2} p^{3} + 2 n^{2} p^{2} + n p^{3} - 2 n p^{2} + n p

\frac{- x + a}{( a + ab ) ( - ba + a )}

(6 x + 3 y = 1, 8) (x + y = 4)

(3 x^{2} - 14 x + 16) \circ (x - 5)

\frac{3}{( 5 - 4 x ) ^{4}}

What is expand np*(np-p+1)^2 ?
The solution to expand np*(np-p+1)^2 is n^3p^3-2n^2p^3+2n^2p^2+np^3-2np^2+np