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