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(x+2)(x+8)

2 min read Jun 16, 2024
(x+2)(x+8)

Expanding the Expression (x+2)(x+8)

The expression (x+2)(x+8) represents the product of two binomials. To expand this expression, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last, and it helps us systematically multiply the terms of the binomials.

Steps to Expand using FOIL

  1. First: Multiply the first terms of each binomial: x * x = x²
  2. Outer: Multiply the outer terms of the binomials: x * 8 = 8x
  3. Inner: Multiply the inner terms of the binomials: 2 * x = 2x
  4. Last: Multiply the last terms of the binomials: 2 * 8 = 16

Now we have: x² + 8x + 2x + 16

Combining Like Terms

The final step is to combine the like terms, which are the terms with the same variable and exponent:

x² + 8x + 2x + 16 = x² + 10x + 16

Conclusion

Therefore, the expanded form of the expression (x+2)(x+8) is x² + 10x + 16. This expression represents a quadratic equation, which can be used to solve for the value of x.

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