What is the standard form of y= (x+5)(x-2)^2 ?

1 Answer
smendyka
Jul 12, 2017

See a solution process below:

Explanation:

First, expand the term being squared on the right hand of the equation using this rule:

(a - b)^2 = a^2 - 2ab + b^2

Substituting x for a and 2 for b gives:

y = (x + 5)(x - 2)^2

y = (x + 5)(x^2 - (2 * x * 2) + 2^2)

y = (x + 5)(x^2 - 4x + 4)

Next, we can multiply the two remaining terms by multiplying each term in the parenthesis on the left by each term in the parenthesis on the left:

y = (color(red)(x) + color(red)(5))(color(blue)(x^2) - color(blue)(4x) + color(blue)(4))

Becomes:

(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(4x)) + (color(red)(x) xx color(blue)(4)) + (color(red)(5) xx color(blue)(x^2)) - (color(red)(5) xx color(blue)(4x)) + (color(red)(5) xx color(blue)(4))

y = x^3 - 4x^2 + 4x + 5x^2 - 20x + 20

We can now group and combine like terms in descending order by the power of the exponent for the x variables::

y = x^3 - 4x^2 + 5x^2 + 4x - 20x + 20

y = x^3 + 1x^2 + (-16)x + 20

y = x^3 + x^2 - 16x + 20

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