clara found the product of 3 - 6y² and y² + 2. her work is shown below. (3 - 6y²)(y² + 2)=3(y²)+(-6y²)(2)=3y²…

clara found the product of 3 - 6y² and y² + 2. her work is shown below. (3 - 6y²)(y² + 2)=3(y²)+(-6y²)(2)=3y² - 12y²=-9y² is the students work correct? no, she did not multiply -6y² by 2 correctly. no, she did not add 3y² and -12y² correctly. no, she did not use the distributive property correctly. yes, she multiplied the binomials correctly.

clara found the product of 3 - 6y² and y² + 2. her work is shown below. (3 - 6y²)(y² + 2)=3(y²)+(-6y²)(2)=3y² - 12y²=-9y² is the students work correct? no, she did not multiply -6y² by 2 correctly. no, she did not add 3y² and -12y² correctly. no, she did not use the distributive property correctly. yes, she multiplied the binomials correctly.

Answer

Explanation:

Step1: Recall distributive property

The distributive property for ((a + b)(c + d)=a(c + d)+b(c + d)=ac+ad+bc+bd). For ((3 - 6y^{2})(y^{2}+2)), it should be (3(y^{2}+2)-6y^{2}(y^{2}+2)=3y^{2}+6-6y^{4}-12y^{2}).

Step2: Analyze student's work

The student only did (3(y^{2})+(- 6y^{2})(2)), missing the multi - plications (3\times2) and (-6y^{2}\times y^{2}). So, the student did not use the distributive property correctly.

Answer:

No, she did not use the distributive property correctly.