Math  /  Algebra

QuestionProblem 4040^{\circ}
Kiran and Mai are trying to figure out if this equation is an identity: (ab)4=a44a3b+6a2b24ab3+b4(a-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}
Kiran picks several different values for aa and bb to test. For each pair he tries, the left side and the right side have the same value. Since his tests all worked, Kiran thinks the equation is an identity. Mai started by using the distributive property on the expression on the left side. She then arranged the result to look the same as the right side. Since she can write both sides the same way, Mai thinks the equation is an identity. Who do you think had a bettef argument for why the equation is an identity? Explain your reasoning.

Studdy Solution
Mai has the better argument.
Kiran's testing approach doesn't guarantee the equation is *always* true.
Mai's approach, using the distributive property, proves the equation holds for any values of aa and bb.

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord