Solve 2a^2-2ax+3(a-x)^2-a+x=

$$2 a ^ { 2 } - 2 a x + 3 ( a - x ) ^ { 2 } - a + x =$$

Evaluate

$$\left(a-x\right)\left(-3x+5a-1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-x\right)^{2}.

$$2a^{2}-2ax+3\left(a^{2}-2ax+x^{2}\right)-a+x$$

Use the distributive property to multiply 3 by a^{2}-2ax+x^{2}.

$$2a^{2}-2ax+3a^{2}-6ax+3x^{2}-a+x$$

Combine 2a^{2} and 3a^{2} to get 5a^{2}.

$$5a^{2}-2ax-6ax+3x^{2}-a+x$$

Combine -2ax and -6ax to get -8ax.

$$5a^{2}-8ax+3x^{2}-a+x$$

Expand

$$3x^{2}-8ax+x+5a^{2}-a$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-x\right)^{2}.

$$2a^{2}-2ax+3\left(a^{2}-2ax+x^{2}\right)-a+x$$

Use the distributive property to multiply 3 by a^{2}-2ax+x^{2}.

$$2a^{2}-2ax+3a^{2}-6ax+3x^{2}-a+x$$

Combine 2a^{2} and 3a^{2} to get 5a^{2}.

$$5a^{2}-2ax-6ax+3x^{2}-a+x$$

Combine -2ax and -6ax to get -8ax.

$$5a^{2}-8ax+3x^{2}-a+x$$