What is (a+b-c)(x-3)-(b-c-a)(x-3) ?

The solution to (a+b-c)(x-3)-(b-c-a)(x-3) is 2ax-6a

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simplify (a+b-c)(x-3)-(b-c-a)(x-3)

simplify

(a + b - c) (x - 3) - (b - c - a) (x - 3)

2 a x - 6 a

Solution steps

(a + b - c) (x - 3) - (b - c - a) (x - 3)

Expand

(a + b - c) (x - 3) : a x - 3 a + b x - 3 b - c x + 3 c

= a x - 3 a + b x - 3 b - c x + 3 c - (b - c - a) (x - 3)

Expand

- (b - c - a) (x - 3) : - b x + 3 b + c x - 3 c + a x - 3 a

= a x - 3 a + b x - 3 b - c x + 3 c - b x + 3 b + c x - 3 c + a x - 3 a

Group like terms

= a x + a x - 3 a - 3 a + b x - b x - 3 b + 3 b - c x + c x + 3 c - 3 c

Add similar elements:

a x + a x = 2 a x

= 2 a x - 3 a - 3 a + b x - b x - 3 b + 3 b - c x + c x + 3 c - 3 c

Add similar elements:

- 3 a - 3 a = - 6 a

= 2 a x - 6 a + b x - b x - 3 b + 3 b - c x + c x + 3 c - 3 c

Add similar elements:

b x - b x = 0

= 2 a x - 6 a - 3 b + 3 b - c x + c x + 3 c - 3 c

Add similar elements:

- 3 b + 3 b = 0

= 2 a x - 6 a - c x + c x + 3 c - 3 c

Add similar elements:

- c x + c x = 0

= 2 a x - 6 a + 3 c - 3 c

Add similar elements:

3 c - 3 c = 0

= 2 a x - 6 a

- (x + 1)^{2} + 3

- 424

(x + 2)^{2} + 3 (x + 2)

(2 x^{2} + 5 x + 7) + (- 10 x^{2} - 7 x + 1)

5 x - 35

What is (a+b-c)(x-3)-(b-c-a)(x-3) ?
The solution to (a+b-c)(x-3)-(b-c-a)(x-3) is 2ax-6a