Like Terms Examples
There are exercises with like terms plus examples on this page. First of all, consider the following algebraic expression:
8ab + 8ay + xb + xy
The terms are the combinations of numbers and variables that make up the expression.
In the above expression, 8ab is the first term, 8ay is the second term, xb is the third term, and xy is the fourth term.
We can see that 8ab + 8ay have the number 8 and the variable a in common.
The other terms have x in common.
So, a and x are the like terms.
Like Terms - Exercises
Instructions: Group terms together in the following exercises and then factor. When you have finished, check your answers in the next section.1) ab2y – 3a + 9b2y – 27
2) xy3b – 4x + 5y3b – 20
3) a2bc + 2c – 2a2b – 4 =
4) x2byz – 5x2b – 25 + 5yz
5) 2a2b2 + 6a2b + 2a2 – 3b2 – 9b – 3
Like Terms - Answers
1) ab2y – 3a + 9b2y – 27 =(ab2y – 3a) + (9b2y – 27) =
[(a × b2 × y) – (3 × a)] + [(9 × b2 × y) – (9 × 3)] =
[(a × b2 × y) – (a × 3)] + [(9 × b2 × y) – (9 × 3)] =
a[(
a[(b2 × y) – (3)] + 9[((b2 × y) – (3)] =
a(b2y – 3) + 9(b2y – 3) =
(b2y – 3)[a(
(b2y – 3)(a + 9)
2) xy3b – 4x + 5y3b – 20 =
(xy3b – 4x) + (5y3b – 20) =
[(x × y3 × b) – (4 × x)] + [(5 × y3 × b) – (4 × 5)] =
[(x × y3 × b) – (x × 4)] + [(5 × y3 × b) – (5 × 4)] =
x[(
x[(y3 × b) – (4)] + 5[(y3 × b) – (4)] =
x(y3b – 4) + 5(y3b – 4) =
(y3b – 4)[x(
(y3b – 4)(x + 5)
3) a2bc + 2c – 2a2b – 4 =
a2bc – 2a2b + 2c – 4 =
[(a2b × c) – (2 × a2b)] + [(2 × c) – (2 × 2)] =
a2b[(
a2b(c – 2) + 2(c – 2) =
(c – 2)[a2b(
(c – 2)(a2b + 2)
4) x2byz – 5x2b – 25 + 5yz =
x2byz + 5yz – 5x2b – 25 =
[(x2b × yz) + 5yz] – (5x2b + 25) =
[(x2b × yz) + (5 × yz)] – [(5 × x2b) + (5 × 5)] =
yz[(x2b
yz[(x2b + 5) – 5(x2b + 5)] =
(x2b + 5)[ yz(
(x2b + 5)(yz – 5)
5) 2a2b2 + 6a2b + 2a2 – 3b2 – 9b – 3 =
(2a2b2 + 6a2b + 2a2) – (3b2 + 9b + 3) =
[2a2b2 + (2a2 × 3 × b) + (2a2 × 1)] – [3b2 + (3 × 3 × b) + (3 × 1)] =
2a2[
(b2 + 3b + 1)[2a2(
(b2 + 3b + 1)(2a2 – 3)
What are Like Terms?
Like terms are the parts of an algebraic expression that have something in common. The like terms may have a number or a product in common.
Alternatively, they may have a variable or a variable raised to a certain power in common.
Grouping Like Terms - More Examples
Factoring becomes much easier when we group like terms together.
Let's look at our example expression again:
8ab + 8ay + xb + xy
You need to follow the steps shown below in order to group like terms and factor your expression.
STEP 1:
Group the terms into two parts, using two sets of parentheses.
8ab + 8ay + xb + xy =
(8ab + 8ay) + (xb + xy)
STEP 2:
Look for the greatest common factor in each group and factor each set of parentheses.
(8ab + 8ay) + (xb + xy) =
[(8a × b) + (8a × y)] + [(x × b) + (x × y)] =
8a[(8a × b) + (8a × y)] + x[(x × b) + (x × y)] =
[8a(b + y)] + [x(b + y)]
STEP 3:
Identify the new greatest common factor.
[8a(b + y)] + [x(b + y)]
From the re-written expression above, we can see that (b + y) is our new greatest common factor.
STEP 4:
Factor out the new greatest common factor.
[8a(b + y)] + [x(b + y)] =
8a(b + y) + x(b + y) =
(b + y)[8a(b + y) + x(b + y)] =
(b + y)(8a + x)
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