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Substitution

Simplifying Before Substituting

As you can see, the values of b and c are different for this problem:

b = -3, c = 2
b2c + bc2 + 2b ?? bc

On the previous page, the expression could not be simplified before its variables, b and c, were substituted with their values.

Whenever possible, an expression should be simplified before substitution is applied, as it will often save time. Begin by simplifying multiplication: "2b ?? bc" becomes "2b2c".

b2c + bc2 + 2b2c

Now combine like terms: b2c and 2b2c are combined into 3b2c.

3b2c + bc2

The problem is now simplified to the following:

b = -3, c = 2
3b2c + bc2

We will begin the substition in a moment, but first compare this expression to the expression we started with. Both expressions are equivalent because we simplified properly. But, by reducing the number of terms in the expression, the substitution step will be easier.

Now substitute b with (-3) and c with (2).

3(-3)2(2) + (-3)(2)2

Use the Order of Operations to simplify the expression. First simplify exponents.

3(9)(2) + (-3)(4)

Simplify multiplication.

3(18) + -12
54 - 12

Combine like terms.

42

The next page briefly explains two variations of the types of substitution problems shown.


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