Expand: (x-3)^2

Question

(A) x²-3x+9

(B) x²-9

(C) x²+3x+9

(D) x²+9

(E) None of these

Answer 1

(x-3)^2

Using the FOIL method gives us...

(x)(x) - (3)(x) - (3)(x) + (-3)(-3) = x^2 - 6x + 9

Thus, the answer is (E).

Answer 2

(x-3)² is the same thing as saying (x-3)(x-3)

Using the FOIL method (First Outside Inside Last) you can begin to expand the equation.

(x-3) (x-3)

. ^-First-^ would be x·x = x²

(x-3) (x-3)

. ^-Outside-^ would be x·(-3) = -3x <--|

. |-- Can be combined because the variable is the same

(x-3) (x-3) | as well as the power to which they're raised -3x-3x = -6x

. ^-Inside-^ would be x·(-3) = -3x <--- |

(x-3) (x-3)

. ^-Last-^ would be (-3)·(-3) = 9

Then you just put the components together: x² - 6x + 9

The quick way to find the square of a function like this is:

(a - b)² = (a² - 2ab +b²) <--- using this one for the problem above where a = x and b = 3

(x)² - 2(x)(3) + (3)² = x² - 6x + 9

or

(a + b)² = (a² + 2ab + b²)