Question

6 simplify the following by collecting like terms.
a \\(3a + 7a\\)
b \\(4n + 3n\\)
c \\(12y - 4y\\)
d \\(5x + 2x + 4x\\)
e \\(6ab - 2ab - ba\\)
f \\(7mn + 2mn - 2mn\\)
g \\(4y - 3y + 8\\)
h \\(7x + 5 - 4x\\)
i \\(6xy + xy + 4y\\)
j \\(5ab + 3 + 7ba\\)
k \\(2 - 5m - m\\)
l \\(4 - 2x + x\\)

Explanation:

Identify like terms in each expression

To simplify algebraic expressions, we identify and group terms that have the exact same variable parts. These are called like terms.

• For a, b, c, d, and f, all terms in each expression are like terms.
• For e, \(ab\) and \(ba\) are like terms because multiplication is commutative, meaning \(ba = ab\).
• For g, h, k, and l, the terms with variables are grouped together, and the constant numbers are grouped separately.
• For i, \(6xy\) and \(xy\) are like terms, while \(4y\) is a different term.
• For j, \(5ab\) and \(7ba\) are like terms, while \(3\) is a constant term.

Combine coefficients of like terms

Using the Algebraic Simplification knowledge point, we add or subtract the coefficients (the numbers in front of the variables) of the like terms:

• a: \(3a + 7a = (3 + 7)a = 10a\)
• b: \(4n + 3n = (4 + 3)n = 7n\)
• c: \(12y - 4y = (12 - 4)y = 8y\)
• d: \(5x + 2x + 4x = (5 + 2 + 4)x = 11x\)
• e: \(6ab - 2ab - 1ab = (6 - 2 - 1)ab = 3ab\)
• f: \(7mn + 2mn - 2mn = (7 + 2 - 2)mn = 7mn\)
• g: \(4y - 3y + 8 = (4 - 3)y + 8 = y + 8\)
• h: \(7x + 5 - 4x = (7 - 4)x + 5 = 3x + 5\)
• i: \(6xy + xy + 4y = (6 + 1)xy + 4y = 7xy + 4y\)
• j: \(5ab + 3 + 7ba = (5 + 7)ab + 3 = 12ab + 3\)
• k: \(2 - 5m - m = 2 - (5 + 1)m = 2 - 6m\)
• l: \(4 - 2x + x = 4 + (-2 + 1)x = 4 - x\)

Answer:

No.	Problem	Answer
b	\(4n + 3n\)	\(7n\)
c	\(12y - 4y\)	\(8y\)
d	\(5x + 2x + 4x\)	\(11x\)
e	\(6ab - 2ab - ba\)	\(3ab\)
f	\(7mn + 2mn - 2mn\)	\(7mn\)
g	\(4y - 3y + 8\)	\(y + 8\)
h	\(7x + 5 - 4x\)	\(3x + 5\)
i	\(6xy + xy + 4y\)	\(7xy + 4y\)
j	\(5ab + 3 + 7ba\)	\(12ab + 3\)
k	\(2 - 5m - m\)	\(2 - 6m\)
l	\(4 - 2x + x\)	\(4 - x\)