Question

Louise completed the work shown below.

(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.


Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

Answer 1

Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

Explanation:

Answer 2

Louise is missing the term
`30x^3`

Explanation:

Remember that the formula for squaring a binomial is:

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

Where

`a` is the first term of the binomial

`b` is the second term of the binomial

Our binomial is
`(5x^3+3)^2`, so
`a=5x^3` and
`b=3`.

Replacing values

`(5x^3+3)^2=(5x^3)^2+2(5x^3)(3)+3^2`

`(5x^3+3)^2=5^2x^6+6(5x^3)+9`

`(5x^3+3)^2=25x^6+30x^3+9`

Since Louise’s answer is
`(5x^3+3)^2=25x^6+9`, we can conclude that she is missing the term
`30x^3`