2-8 Inverse of a Sum and Simplifying Warm-up Problems 1.(–1)(–1) 2.(–1)x 3.(–1)2y 4.(–1)(x + 2) Simplify. 5.[(3 + 5) + 7] (2x + 4x) – 4x (5 + 4) 8.[(7x – 3x) – 2x] + 5x

Chapter Inverse of a Sum and Simplifying

The Property of –1 For any rational number a, (Negative one times a is the additive inverse of a.)

Example 1 Rename each additive inverse without parentheses.

Try This Multiply. a.–(x + 2) b.–(5x + 2y + 8) c.–(a – 7) d.–(3c – 4d + 1)

The Inverse of a Sum of a Property For any rational numbers a and b, (The additive inverse of a sum is the sum of the additive inverses.)

Try This Multiply. e.–(6 – t) f.–(–4a + 3t – 10) g.–(18 – m – 2n + 4t)

Example 2 Simplify.

Try This Multiply. h.5x – (3x + 9) i.5x – 2y – (2y – 3x – 4)

Example 3 Simplify.

Try This Multiply. j.y – 9(x + y) k.5a – 3(7a – 6)

Grouping Symbols Parentheses ( ) Brackets [ ] Braces { }

Try This Multiply. l.3(4 + 2) – {7 – [4 – (6 + 5)]} m.[3(4 + 2) + 2x] – [4(y + 2) – 3(y – 2)]