(x%2B2)(x%2B3).jpeg "(x+1)(x+2)(x+3)")
Expanding (x+1)(x+2)(x+3)
This article will explore the process of expanding the expression (x+1)(x+2)(x+3). This involves multiplying out the factors to get a polynomial in standard form.
Expanding the First Two Factors
We start by multiplying the first two factors:
(x+1)(x+2) = x(x+2) + 1(x+2)
Using the distributive property:
= x² + 2x + x + 2
Combining like terms:
= x² + 3x + 2
Expanding the Entire Expression
Now we need to multiply the result by the third factor:
(x² + 3x + 2)(x+3) = x(x² + 3x + 2) + 3(x² + 3x + 2)
Distributing again:
= x³ + 3x² + 2x + 3x² + 9x + 6
Combining like terms:
= x³ + 6x² + 11x + 6
Conclusion
Therefore, the expanded form of (x+1)(x+2)(x+3) is x³ + 6x² + 11x + 6. This process demonstrates the use of the distributive property and combining like terms in simplifying polynomial expressions.