Question

Does $(y-1)^{3}=y^{3}-1 ?$ Why or why not?

   Does $(y-1)^{3}=y^{3}-1 ?$ Why or why not?

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 6, Problem 122

Instant Answer

Solved by Expert Zain Haider

04/13/2021

Step 1

The binomial theorem states that $(a-b)^{n}=a^{n}-n*a^{n-1}*b+n*(n-1)/2*a^{n-2}*b^{2}-...$ until $b^{n}$. Show more…

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Does $(y-1)^{3}=y^{3}-1 ?$ Why or why not?

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Key Concepts

Binomial Theorem

The Binomial Theorem provides a systematic method for expanding expressions of the form (a + b)^n into a sum that includes terms involving different powers of a and b. It shows that when raising a binomial to a power, all combinations of terms occur with specific coefficients, which is why an expansion like (y-1)^3 results in additional terms beyond just y^3 and -1.

Exponentiation Non-Distributivity

Exponentiation does not distribute over addition or subtraction; that is, (a - b)^n is not equal to a^n - b^n. This principle is crucial when working with polynomial expressions because it ensures that all the cross terms are correctly accounted for in an expanded expression.

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