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

Question

iluvyou23452nwj · Accepted Answer

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

{(a - b)}^{2} = a^{2} - 2 a b + b^{2}

Substituting x for a and 2 for b gives:

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

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

y = (x + 5) (x^{2} - (2 \cdot x \cdot 2) + 2^{2})

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

Becomes:

(x \times x^{2}) - (x \times 4 x) + (x \times 4) + (5 \times x^{2}) - (5 \times 4 x) + (5 \times 4)

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

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

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

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