The factored form of a quadratic is useful for finding the roots and other properties but sometimes it is useful to expand in order to simplify the equation.
Expanding from factored form uses the distributive property of real numbers which states for real numbers x and y,
c (x + y) = cx + cy
Example
Expand and simplify x (x2 + 5).
We apply the distributive property to the equation to expand and then we simplify the resulting equation.
= x (x2 + 5)
= (x)(x2) + (x)(5)
= x3 + 5x
We can also apply the distributive property to equations with the form (x + a)(x + b). This results in the following.
= (x + a)(x + b)
= x2 + ax + bx + ab
= x2 + (a + b)x + ab
Expand and simplify (x + 2)(x + 3).
= (x + 2)(x + 3)
= x2 + 2x + 3x + 2(3)
= x2 + 5x + 6
Expand and simplify (x – 2)(x + 3).
= (x – 2)(x + 3)
= x2 -2x + 3x + (-2)(3)
= x2 + x – 6
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