(x+a)(x-b) Examples

Jasonbradley

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Jun 17, 2024

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Expanding (x+a)(x-b)

The expression (x+a)(x-b) is a common algebraic expression that often appears in math problems. Expanding this expression involves multiplying the two binomials using the FOIL method (First, Outer, Inner, Last).

Here's a breakdown of how to expand (x+a)(x-b):

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * -b = -bx
3. Inner: Multiply the inner terms of the binomials: a * x = ax
4. Last: Multiply the last terms of the binomials: a * -b = -ab

Now, combine all the terms:

(x+a)(x-b) = x² - bx + ax - ab

Simplifying the expression:

You can often simplify the expression by combining the middle terms if they have the same variable. In this case, we can combine -bx and ax:

(x+a)(x-b) = x² + (a-b)x - ab

Example

Let's see an example with specific values for a and b:

Expand (x+3)(x-2)

1. First: x * x = x²
2. Outer: x * -2 = -2x
3. Inner: 3 * x = 3x
4. Last: 3 * -2 = -6

Combining the terms:

(x+3)(x-2) = x² - 2x + 3x - 6

Simplifying:

(x+3)(x-2) = x² + x - 6

Practice Problems

Try expanding these expressions using the same steps:

1. (x+5)(x-1)
2. (x-4)(x+3)
3. (x+7)(x-7)

Remember: The key is to follow the FOIL method and simplify the resulting expression by combining like terms.