Remove parenthesis and simplify.

Question

Remove parentheses and simplify.

A. -3x - (-x +y) 

B. -3( x - 2) - 4x 

C. 10 - 2(5 - 4x)

 

Answer 1

A) The expression is -3x - (-x +y).

= -3x + (-1)(-x +y)

Apply Distribuive Property of Multiplication over Addition: a (b + c) = a b + a c.

= -3x + (-1)(-x ) + (-1)(y)

= -3x + x + (-y)

Product of two different signs is negative.

= -3x + x - y

Combine like terms.

= -2x - y

The solution is -2x - y.

B) The expression is -3(x - 2) - 4x.

Apply Distribuive Property of Multiplication over Subtraction: a (b - c) = a b - a c.

= -3(x) - (-3)(2) - 4x

= -3x - (-6) - 4x

Product of two same signs is positive.

= -3x + 6 - 4x

Group like terms.

= -3x - 4x + 6

Combine like terms.

= -7x + 6

The solution is -7x + 6.

C) The expression is 10 - 2(5 - 4x).

= 10 + (-2)(5 - 4x)

Apply Distribuive Property of Multiplication over Subtraction: a (b - c) = a b - a c.

= 10 + (-2)(5) - (-2)(4x)

= 10 + (-10) - (-8x)

Product of two different signs is negative.

= 10 - 10 - (-8x)

Product of two same signs is positive.

= 10 - 10 + 8x

Apply Additive Inverse Property: a + ( -a ) = 0.

= 0 + 8x

Apply Additive Identity Property: a + 0 = a.

= 8x

The solution 8x.