Expanding and Simplifying the Expression (x+5)(x+6)(x3)(x+7)
This article will walk through the process of expanding and simplifying the algebraic expression: (x+5)(x+6)(x3)(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

(x3)(x+7):
 x * x = x²
 x * 7 = 7x
 3 * x = 3x
 3 * 7 = 21
 (x3)(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)(x3)(x+7) to 7x + 51.