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

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

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expand (np-p+1)^2

expand

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

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

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= (n p - p + 1) (n p - p + 1)

Distribute parentheses

= n p n p + n p (- p) + n p \cdot 1 - p n p - p (- p) - p \cdot 1 + 1 \cdot n p + 1 \cdot (- p) + 1 \cdot 1

Simplify

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

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

- \frac{( x + h ) ^{4}}{4 h}

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

\frac{5}{( 3 x - 2 ) ^{2}}

\frac{( x - 4 ) ( x + 1 )}{x - 3}

\frac{x ^{2} ( x + 1 )}{x + 2}

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