(x%2B17)-in-standard-form.jpeg "(x+1)(x+17) In Standard Form")
Expanding (x+1)(x+17) into Standard Form
In mathematics, the standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants. To express the product (x+1)(x+17) in standard form, we need to expand it using the distributive property (also known as FOIL).
Expanding Using FOIL
FOIL stands for First, Outer, Inner, Last, and it helps us remember the steps for multiplying two binomials. Let's break down the expansion:
-
First: Multiply the first terms of each binomial: x * x = x²
-
Outer: Multiply the outer terms of the binomials: x * 17 = 17x
-
Inner: Multiply the inner terms of the binomials: 1 * x = x
-
Last: Multiply the last terms of each binomial: 1 * 17 = 17
Now, we combine all the terms: x² + 17x + x + 17
Simplifying the Expression
Finally, we combine the like terms (the terms with 'x'): x² + 18x + 17
Therefore, the standard form of the expression (x+1)(x+17) is x² + 18x + 17.