Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

To solve the given problems involving adding and subtracting monomials, we need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power(s). Here's the step-by-step solution for each problem:

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1. First Row:

#### (a) \( 3a - 2a \)
- Both terms have the same variable \( a \).
- Combine the coefficients: \( 3 - 2 = 1 \).
- Result: \( 1a = a \).

#### (b) \( v - 4v \)
- Both terms have the same variable \( v \).
- Combine the coefficients: \( 1 - 4 = -3 \).
- Result: \( -3v \).

#### (c) \( 9x - 7x \)
- Both terms have the same variable \( x \).
- Combine the coefficients: \( 9 - 7 = 2 \).
- Result: \( 2x \).

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2. Second Row:

#### (a) \( 2c + 3c \)
- Both terms have the same variable \( c \).
- Combine the coefficients: \( 2 + 3 = 5 \).
- Result: \( 5c \).

#### (b) \( k - (-4k) \)
- Simplify the subtraction of a negative: \( k + 4k \).
- Combine the coefficients: \( 1 + 4 = 5 \).
- Result: \( 5k \).

#### (c) \( -3r + 4r \)
- Both terms have the same variable \( r \).
- Combine the coefficients: \( -3 + 4 = 1 \).
- Result: \( 1r = r \).

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3. Third Row:

#### (a) \( 2\sqrt{2}n - (\sqrt{2}n) \)
- Both terms have the same variable \( n \) and the same coefficient factor \( \sqrt{2} \).
- Combine the coefficients: \( 2 - 1 = 1 \).
- Result: \( 1\sqrt{2}n = \sqrt{2}n \).

#### (b) \( -n - 7n \)
- Both terms have the same variable \( n \).
- Combine the coefficients: \( -1 - 7 = -8 \).
- Result: \( -8n \).

#### (c) \( -2q^2 + 2q^2 \)
- Both terms have the same variable \( q^2 \).
- Combine the coefficients: \( -2 + 2 = 0 \).
- Result: \( 0 \).

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4. Fourth Row:

#### (a) \( -2b^2 - 5b^2 \)
- Both terms have the same variable \( b^2 \).
- Combine the coefficients: \( -2 - 5 = -7 \).
- Result: \( -7b^2 \).

#### (b) \( 2m^2n^2 + 6m^2n^2 \)
- Both terms have the same variables \( m^2n^2 \).
- Combine the coefficients: \( 2 + 6 = 8 \).
- Result: \( 8m^2n^2 \).

#### (c) \( 2t - 10t \)
- Both terms have the same variable \( t \).
- Combine the coefficients: \( 2 - 10 = -8 \).
- Result: \( -8t \).

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5. Fifth Row:

#### (a) \( -2p + 4p \)
- Both terms have the same variable \( p \).
- Combine the coefficients: \( -2 + 4 = 2 \).
- Result: \( 2p \).

#### (b) \( 8a + 3a \)
- Both terms have the same variable \( a \).
- Combine the coefficients: \( 8 + 3 = 11 \).
- Result: \( 11a \).

#### (c) \( -y - 6y \)
- Both terms have the same variable \( y \).
- Combine the coefficients: \( -1 - 6 = -7 \).
- Result: \( -7y \).

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6. Sixth Row:

#### (a) \( -2y^2 + 5y^2 \)
- Both terms have the same variable \( y^2 \).
- Combine the coefficients: \( -2 + 5 = 3 \).
- Result: \( 3y^2 \).

#### (b) \( 2v^3 - 5v^3 \)
- Both terms have the same variable \( v^3 \).
- Combine the coefficients: \( 2 - 5 = -3 \).
- Result: \( -3v^3 \).

#### (c) \( a^2b + 4a^2b \)
- Both terms have the same variables \( a^2b \).
- Combine the coefficients: \( 1 + 4 = 5 \).
- Result: \( 5a^2b \).

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7. Seventh Row:

#### (a) \( 2q - 4q \)
- Both terms have the same variable \( q \).
- Combine the coefficients: \( 2 - 4 = -2 \).
- Result: \( -2q \).

#### (b) \( 5c - 8c \)
- Both terms have the same variable \( c \).
- Combine the coefficients: \( 5 - 8 = -3 \).
- Result: \( -3c \).

#### (c) \( 3j^5 + 5j^5 \)
- Both terms have the same variable \( j^5 \).
- Combine the coefficients: \( 3 + 5 = 8 \).
- Result: \( 8j^5 \).

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Final Answer:

\[
\boxed{
\begin{array}{ccc}
a & -3v & 2x \\
5c & 5k & r \\
\sqrt{2}n & -8n & 0 \\
-7b^2 & 8m^2n^2 & -8t \\
2p & 11a & -7y \\
3y^2 & -3v^3 & 5a^2b \\
-2q & -3c & 8j^5 \\
\end{array}
}
\]