(x%2B6)-(x-3)(x%2B7).jpeg "(x+5)(x+6)-(x-3)(x+7)")
Expanding and Simplifying the Expression (x+5)(x+6)-(x-3)(x+7)
This article will walk through the process of expanding and simplifying the algebraic expression: (x+5)(x+6)-(x-3)(x+7).
Expanding the Expressions
We can simplify this expression by using the distributive property (also known as FOIL method) to expand each of the multiplications:
-
(x+5)(x+6):
- x * x = x²
- x * 6 = 6x
- 5 * x = 5x
- 5 * 6 = 30
- (x+5)(x+6) = x² + 6x + 5x + 30
-
(x-3)(x+7):
- x * x = x²
- x * 7 = 7x
- -3 * x = -3x
- -3 * 7 = -21
- (x-3)(x+7) = x² + 7x - 3x - 21
Combining the Expanded Expressions
Now we can substitute these expanded expressions back into our original equation:
(x² + 6x + 5x + 30) - (x² + 7x - 3x - 21)
Simplifying the Expression
To simplify, we combine like terms:
- x² - x² = 0
- 6x + 5x - 7x + 3x = 7x
- 30 + 21 = 51
Therefore, the simplified expression is: 7x + 51
Conclusion
By applying the distributive property and combining like terms, we successfully simplified the expression (x+5)(x+6)-(x-3)(x+7) to 7x + 51.