In Part 2 of our lesson series on Algebra, this lesson focuses on expanding algebraic equations with exponents. An exponent is a small number placed to the right of a larger number to show how many times that number needs to be multiplied by itself.

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## Expanding Algebraic Equations With Exponents

An exponent is a small number placed to the right of a larger number to show how many times that number needs to be multiplied by itself.

For example, b^{3} means to multiply b by itself three times.

In mathematical terms, this becomes b x b x b

When we expand algebraic equations with exponents, we multiply the entire equation by itself. Let’s review with some examples.

**Example 1.** Expand (a + b)^{2}

**Step 1.** First rewrite the expression without the exponent. Look at the “power” of the exponent, i.e. what number is written to the right of the equation, to determine how many times the equation needs to be multiplied by itself. In this example, the exponent is ‘2’, so we need to multiply the equation by itself twice.

**Step 2.** Next, distribute (another word for multiply) the ‘a’ from the first parenthesis to both of the variables in the second parenthesis. Then, distribute the ‘b’ from the first parenthesis to both of the variables in the second parenthesis.

**Step 3.** Simplify. Since ab is mathematically equivalent to ba, we can rewrite ad + ba as 2ba

** a ^{2 }+ 2ab + b^{2}**

Confused? Let’s try a similar problem with real numbers.

**Example 2.** Expand (2x – 3)^{2}

**Step 1.** First rewrite the expression without the exponents. Since the exponent is the number 2, we multiply the expression by itself twice.

**Step 2.** Distribute the ‘2x’ from the first parenthesis to both of the variables in the second parenthesis. Then, distribute the ‘3’ from the first parenthesis to both the variables in the second parenthesis.

**Step 3.** Simplify. In this instance, 2x times 2x becomes (2 times 2) (x times x) or 4 x2A

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