simplify (2p + 3q)2 - (p - q)(2q - p)

asked by guest
on Nov 23, 2024 at 12:38 am



You asked:

Simplify the expression: (2p+3q)⋅2−(p−q)(2q−p)\left(2 p + 3 q\right) \cdot 2 - \left(p - q\right) \left(2 q - p\right)

MathBot Answer:

Simplified:

(2p+3q)⋅2−(p−q)(2q−p)=4p+6q+(p−2q)(p−q) \left(2 p + 3 q\right) \cdot 2 - \left(p - q\right) \left(2 q - p\right) = 4 p + 6 q + \left(p - 2 q\right) \left(p - q\right)

(2p+3q)2−(2q−p)(p−q)=−(−2q2−p2+3pq)+(2p+3q)2=−(−2q2−p2+3pq)+4p+6q=p2+2q2−3pq+4p+6q=4p+6q+(p−2q)(p−q)\begin{aligned}\left(2 p + 3 q\right) 2 - \left(2 q - p\right) \left(p - q\right)&=-\left(- 2 q^{2} - p^{2} + 3 p q\right) + \left(2 p + 3 q\right) 2\\&=-\left(- 2 q^{2} - p^{2} + 3 p q\right) + 4 p + 6 q\\&=p^{2} + 2 q^{2} - 3 p q + 4 p + 6 q\\&=4 p + 6 q + \left(p - 2 q\right) \left(p - q\right)\end{aligned}

Expanded:

(2p+3q)⋅2−(p−q)(2q−p)=p2−3pq+4p+2q2+6q \left(2 p + 3 q\right) \cdot 2 - \left(p - q\right) \left(2 q - p\right) = p^{2} - 3 p q + 4 p + 2 q^{2} + 6 q

Factored:

(2p+3q)⋅2−(p−q)(2q−p)=p2−3pq+4p+2q2+6q \left(2 p + 3 q\right) \cdot 2 - \left(p - q\right) \left(2 q - p\right) = p^{2} - 3 p q + 4 p + 2 q^{2} + 6 q


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