Question

foundations 2
combining like terms quiz review
simplify each expression.

1. $5k + 8 + 10k$ \t\t\t\t\t 2) $1 + 10x + 2$

1. $-7m + 10m - 8$ \t\t\t\t 4) $p - 10 + 4p$

1. $3b + 9 + 2 + 9b$ \t\t\t\t 6) $-8p + 8 + 8p + 10$

1. $1 - 9b + 3 + 6b$ \t\t\t\t 8) $10 - 3v + 3 + 2v$

1. $1 + 8b + 6 - 6b$ \t\t\t\t 10) $k - 10 + k - 6$

Explanation:

Step1: Combine like terms for \(5k + 8 + 10k\)

Identify like terms (\(5k\) and \(10k\)). Add their coefficients: \(5k + 10k = 15k\). The constant term is \(8\). So the simplified expression is \(15k + 8\).

Step2: Combine like terms for \(1 + 10x + 2\)

Identify like terms (\(1\) and \(2\)). Add them: \(1 + 2 = 3\). The term with \(x\) is \(10x\). So the simplified expression is \(10x + 3\).

Step3: Combine like terms for \(-7m + 10m - 8\)

Identify like terms (\(-7m\) and \(10m\)). Add their coefficients: \(-7m + 10m = 3m\). The constant term is \(-8\). So the simplified expression is \(3m - 8\).

Step4: Combine like terms for \(p - 10 + 4p\)

Identify like terms (\(p\) and \(4p\)). Add their coefficients: \(p + 4p = 5p\). The constant term is \(-10\). So the simplified expression is \(5p - 10\).

Step5: Combine like terms for \(3b + 9 + 2 + 9b\)

Identify like terms (\(3b\) and \(9b\), \(9\) and \(2\)). Add coefficients of \(b\): \(3b + 9b = 12b\). Add constants: \(9 + 2 = 11\). So the simplified expression is \(12b + 11\).

Step6: Combine like terms for \(-8p + 8 + 8p + 10\)

Identify like terms (\(-8p\) and \(8p\), \(8\) and \(10\)). Add coefficients of \(p\): \(-8p + 8p = 0\). Add constants: \(8 + 10 = 18\). So the simplified expression is \(18\).

Step7: Combine like terms for \(1 - 9b + 3 + 6b\)

Identify like terms (\(-9b\) and \(6b\), \(1\) and \(3\)). Add coefficients of \(b\): \(-9b + 6b = -3b\). Add constants: \(1 + 3 = 4\). So the simplified expression is \(-3b + 4\).

Step8: Combine like terms for \(10 - 3v + 3 + 2v\)

Identify like terms (\(-3v\) and \(2v\), \(10\) and \(3\)). Add coefficients of \(v\): \(-3v + 2v = -v\). Add constants: \(10 + 3 = 13\). So the simplified expression is \(-v + 13\) (or \(13 - v\)).

Step9: Combine like terms for \(1 + 8b + 6 - 6b\)

Identify like terms (\(8b\) and \(-6b\), \(1\) and \(6\)). Add coefficients of \(b\): \(8b - 6b = 2b\). Add constants: \(1 + 6 = 7\). So the simplified expression is \(2b + 7\).

Step10: Combine like terms for \(k - 10 + k - 6\)

Identify like terms (\(k\) and \(k\), \(-10\) and \(-6\)). Add coefficients of \(k\): \(k + k = 2k\). Add constants: \(-10 - 6 = -16\). So the simplified expression is \(2k - 16\).

Answer:

1. \(15k + 8\)
2. \(10x + 3\)
3. \(3m - 8\)
4. \(5p - 10\)
5. \(12b + 11\)
6. \(18\)
7. \(-3b + 4\)
8. \(13 - v\) (or \(-v + 13\))
9. \(2b + 7\)
10. \(2k - 16\)