Expanding and Simplifying the Expression (x+4)(x2)(x3)^2
This article will guide you through the process of expanding and simplifying the algebraic expression (x+4)(x2)(x3)^2.
Expanding the Expressions

(x+4)(x2): This is a product of two binomials. We can expand it using the FOIL method (First, Outer, Inner, Last):
 First: x * x = x²
 Outer: x * 2 = 2x
 Inner: 4 * x = 4x
 Last: 4 * 2 = 8
 Combine the terms: x²  2x + 4x  8 = x² + 2x  8

(x3)^2: This is a squared binomial. We can expand it by multiplying it with itself:
 (x3)(x3)
 First: x * x = x²
 Outer: x * 3 = 3x
 Inner: 3 * x = 3x
 Last: 3 * 3 = 9
 Combine the terms: x²  3x  3x + 9 = x²  6x + 9
Simplifying the Expression
Now we have: (x+4)(x2)(x3)^2 = (x² + 2x  8)  (x²  6x + 9)
To simplify further, distribute the negative sign: x² + 2x  8  x² + 6x  9
Finally, combine like terms: (x²  x²) + (2x + 6x) + (8  9) = 8x  17
Conclusion
Therefore, the simplified form of the expression (x+4)(x2)(x3)^2 is 8x  17.