What is (p+q-r)^2-(p-q+r)^2 ?

The solution to (p+q-r)^2-(p-q+r)^2 is 4pq-4pr

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simplify (p+q-r)^2-(p-q+r)^2

simplify

(p + q - r)^{2} - (p - q + r)^{2}

4 pq - 4 p r

Solution steps

(p + q - r)^{2} - (p - q + r)^{2}

Expand

(p + q - r)^{2} : p^{2} + 2 pq - 2 p r + q^{2} - 2 q r + r^{2}

= p^{2} + 2 pq - 2 p r + q^{2} - 2 q r + r^{2} - (p - q + r)^{2}

Expand

- (p - q + r)^{2} : - p^{2} + 2 pq - 2 p r - q^{2} + 2 q r - r^{2}

= p^{2} + 2 pq - 2 p r + q^{2} - 2 q r + r^{2} - p^{2} + 2 pq - 2 p r - q^{2} + 2 q r - r^{2}

Group like terms

= p^{2} - p^{2} + 2 pq + 2 pq - 2 p r - 2 p r + q^{2} - q^{2} - 2 q r + 2 q r + r^{2} - r^{2}

Add similar elements:

p^{2} - p^{2} = 0

= 2 pq + 2 pq - 2 p r - 2 p r + q^{2} - q^{2} - 2 q r + 2 q r + r^{2} - r^{2}

Add similar elements:

2 pq + 2 pq = 4 pq

= 4 pq - 2 p r - 2 p r + q^{2} - q^{2} - 2 q r + 2 q r + r^{2} - r^{2}

Add similar elements:

- 2 p r - 2 p r = - 4 p r

= 4 pq - 4 p r + q^{2} - q^{2} - 2 q r + 2 q r + r^{2} - r^{2}

Add similar elements:

q^{2} - q^{2} = 0

= 4 pq - 4 p r - 2 q r + 2 q r + r^{2} - r^{2}

Add similar elements:

- 2 q r + 2 q r = 0

= 4 pq - 4 p r + r^{2} - r^{2}

Add similar elements:

r^{2} - r^{2} = 0

= 4 pq - 4 p r

m^{4} - 14 m^{2} + 1

- 5 x + (- x)

- t - 77

\frac{27 z ^{5}}{30 z ^{4}}

\frac{( 6 c ^{4} - 3 c ^{2} - 3 c )}{( 3 c )}