(x%2B7)-(x%2B2)(x%2B3).jpeg "(x+1)(x+7)-(x+2)(x+3)")
Expanding and Simplifying the Expression (x+1)(x+7)-(x+2)(x+3)
This article will guide you through expanding and simplifying the given expression: (x+1)(x+7)-(x+2)(x+3).
Expanding the Expression
The expression involves multiplying two binomials, so we can use the distributive property (or FOIL method) to expand each set of parentheses:
Step 1: Expand the first set of parentheses: (x+1)(x+7) = x(x+7) + 1(x+7) = x² + 7x + x + 7 = x² + 8x + 7
Step 2: Expand the second set of parentheses: (x+2)(x+3) = x(x+3) + 2(x+3) = x² + 3x + 2x + 6 = x² + 5x + 6
Step 3: Substitute the expanded terms back into the original expression: (x+1)(x+7)-(x+2)(x+3) = (x² + 8x + 7) - (x² + 5x + 6)
Simplifying the Expression
Now we have: (x² + 8x + 7) - (x² + 5x + 6)
Step 1: Distribute the negative sign: x² + 8x + 7 - x² - 5x - 6
Step 2: Combine like terms: (x² - x²) + (8x - 5x) + (7 - 6) = 3x + 1
Conclusion
Therefore, the simplified form of the expression (x+1)(x+7)-(x+2)(x+3) is 3x + 1.