To expand the expression [tex]\((x-9)(x-1)\)[/tex] using the distributive property, also known as the FOIL method, follow these steps:
1. Multiply the first terms: [tex]\( x \cdot x = x^2 \)[/tex].
2. Multiply the outer terms: [tex]\( x \cdot (-1) = -x \)[/tex].
3. Multiply the inner terms: [tex]\( -9 \cdot x = -9x \)[/tex].
4. Multiply the last terms: [tex]\( -9 \cdot (-1) = 9 \)[/tex].
Now, combine all these products:
[tex]\[
x^2 + (-x) + (-9x) + 9
\][/tex]
Next, combine the like terms:
[tex]\[
x^2 + (-x - 9x) + 9 = x^2 - 10x + 9
\][/tex]
So, when we use the distributive property to expand [tex]\((x-9)(x-1)\)[/tex], we get:
[tex]\[
x^2 + (-10)x + 9
\][/tex]
Thus, the complete expanded expression is:
[tex]\[
x^2 - 10x + 9
\][/tex]
