-(x%2Bb)-answer.jpeg "(x+a) (x+b) Answer")
Expanding (x + a)(x + b)
The expression (x + a)(x + b) is a common algebraic expression that represents the product of two binomials. Expanding this expression involves using the distributive property, also known as FOIL (First, Outer, Inner, Last).
Understanding FOIL
FOIL is a mnemonic device to help remember the steps of expanding the product of two binomials:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Expanding (x + a)(x + b)
Following the FOIL method:
- First: x * x = x²
- Outer: x * b = bx
- Inner: a * x = ax
- Last: a * b = ab
Therefore, the expanded form of (x + a)(x + b) is:
(x + a)(x + b) = x² + bx + ax + ab
Simplifying the Expression
The expanded expression can be further simplified by combining the like terms (bx and ax):
(x + a)(x + b) = x² + (b + a)x + ab
Conclusion
Expanding (x + a)(x + b) involves using the distributive property (FOIL method) to multiply the terms of the binomials. The resulting expression can be simplified by combining like terms, leading to a more compact form. Understanding this expansion is fundamental for solving various algebraic problems and equations.