A term of an algebraic expression is the prduct of numbers and variables. For example, 2c is a term formed by the product of the number 2 and the variable c. The number 2 which is attached to the variable c is called the coefficient of c. For the simple expression c, the coefficient is 1.
A term consists of a coefficient with an unknown.
For example, 2f is a term.
2 is a constant, while f is a variable.
A term which has no unknown or variable is called a constant.
For example, 3 is a constant in the expression 3 + a.
A polynomial may be the sum of difference of terms. For example, 2x + 3x is an expression with two terms or a binomial. 2x and 3x are called like terms as they have common unknown x.
Terms which are not like terms are unlike terms such as 6x2 and x3, as they have different unknowns.
Only like terms can be collected by addition or subtraction.
Let us look at the distributive property below.
a(b + c) = ab + ac
The left-hand side (LHS) is in the form of a product: a(b + c)
The right-hand side (RHS) is in the form of a sum: ab + ac
Using the distributive property, we can convert an expression from one form to another.
How do we remove the parentheses of the following expression?
5x + 2(y - 5x) + 3b - (a - 4b)
Product - Sum
2(y - 4x) 2y - 8x
Notice that we expand the "product" to get the sum. In this process, we have removed the grouping symbols.
Let us interpret this expression as:
3b + (-1) (a - 4b)
So, 3b - (a - 4b) = 3b + (-1) (a - 4b)
3b + (-1) (a + (-1) - 4b)
3b - (a + 4b)
Now, we write:
5x + 2(y - 4x) + 3b - (a - 4b) = 5x +2y - 8x +3b - a + 4b
= 2y - 3x - a +7b
Rules in removing grouping symbols:
Let us move on to another topic, just click here! Lesson 5 Multiplication of Polynomials
If you are ready to answer activities, just click here! Basic Algebra Tests
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