Question

multiplying a binomial by a binomial

clara found the product of (3 - 6y^2) and (y^2 + 2). her work is shown below.

((3 - 6y^2)(y^2 + 2) = 3(y^2) + (-6y^2)(2))
(= 3y^2 - 12y^2)
(= -9y^2)

is the students work correct?

no, she did not multiply (-6y^2) by 2 correctly.
no, she did not add (3y^2) and (-12y^2) correctly.
no, she did not use the distributive property correctly.
yes, she multiplied the binomials correctly.

Explanation:

Analyze the student's multiplication setup

$$ (3 - 6y^2)(y^2 + 2) = 3(y^2) + (-6y^2)(2) $$

Evaluate the application of the distributive property

$$ (a + b)(c + d) = ac + ad + bc + bd $$

$$ (3 - 6y^2)(y^2 + 2) = 3(y^2) + 3(2) + (-6y^2)(y^2) + (-6y^2)(2) $$

Identify the error in the student's work

The student only calculated two terms instead of four, missing the products \(3(2)\) and \((-6y^2)(y^2)\).

Answer:

• No, she did not multiply \(-6y^2\) by 2 correctly.
• No, she did not add \(3y^2\) and \(-12y^2\) correctly.
• No, she did not use the distributive property correctly. (Correct answer)
• Yes, she multiplied the binomials correctly.