Algebra (GROUPING SYMBOLS)

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify [Q - R] + [S - T].

10m + 7n - 14

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify Q - [R + S] - T.

10m - 7n - 14

like terms

terms that have the same variable(s), with each variable raised to the same exponent

Simplify -(-2a + 13) + (-9a - 2) - (-7a - 3).

-12

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify R - [S + T].

-m + 2n - 2

Simplify 3j - {2k - [5h - (3j + k)]}.

5h - 3k

Review

Polynomials may be added and subtracted vertically or horizontally. The distributive property is used to add and subtract polynomials horizontally. If the grouping symbol is preceded by a + sign, just remove the grouping symbols. If the grouping symbol is preceded by a - sign, change the sign on each term as you remove the grouping symbols.

polynomial

a term or a sum of terms whose variables have whole number exponents

distributive property

a(b + c) = ab + ac or a(b - c) = ab - ac

Simplify {n - 1 - [n - 1 - (n - 1)]}.

n-1

Simplify (3x + 5) + (2x - 9) - (4x + 3).

x - 7

Simplify (x - y + 1) - (x + y - 1).

-2y+2

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify R - S + T.

-3m - 4n + 14

Simplify 2m - [n - (m - 2n)].

3m - 3n

Simplify n - {1 - [n - (1 - n) - 1]}.

3n - 3

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify Q + S - T.

8m + 7n - 3

Simplify a - {5b - [a - (3b - 2c) + c - (a - 2b - c)]}.

a - 6b + 4c