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Expanding the Expression (x+8)(x+7)
In algebra, expanding an expression means writing it in a simpler form without any parentheses. The expression (x+8)(x+7) represents the product of two binomials. To expand it, we can use the distributive property, also known as the FOIL method.
FOIL Method
FOIL stands for First, Outer, Inner, and Last. It's a mnemonic device to help us remember the steps involved in multiplying two binomials.
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 7 = 7x
- Inner: Multiply the inner terms of the binomials: 8 * x = 8x
- Last: Multiply the last terms of each binomial: 8 * 7 = 56
Now, we add all these products together:
x² + 7x + 8x + 56
Finally, combine the like terms:
x² + 15x + 56
Therefore, the expanded form of (x+8)(x+7) is x² + 15x + 56.