What is (a+b+c)-(a-b+c-d) ?

The solution to (a+b+c)-(a-b+c-d) is 2b+d

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simplify (a+b+c)-(a-b+c-d)

simplify

(a + b + c) - (a - b + c - d)

2 b + d

Solution steps

(a + b + c) - (a - b + c - d)

Apply rule:

(a) = a

(a + b + c) = a + b + c

= a + b + c - (a - b + c - d)

Apply the distributive law:

- (a - b) = - a + b

- (a - b + c - d) = - a + b - c + d

= a + b + c - a + b - c + d

Group like terms

= a - a + b + b + c - c + d

Add similar elements:

a - a = 0

= b + b + c - c + d

Add similar elements:

b + b = 2 b

= 2 b + c - c + d

Add similar elements:

c - c = 0

= 2 b + d

25 k^{2} - 16

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∣ 9 x ∣ < - 5

\frac{x ^{5} x ^{- 5}}{y ^{3} y ^{- 2}}