Exercises: Apply the Binomial Theorem

This is an advanced (+) topic. Work through each section in order, showing all steps for expansion problems.

Grade 11·21 problems·~42 min·Common Core Math - HS Algebra·standard·hsa-apr-c-5

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Fluency Practice

$Pascal's Triangle rows 0 through 5, with Row 5 highlighted and the entry C(5,2)=10 circled to show the coefficient of x^3y^2 in (x+y)^5.$

Which entry in Pascal's Triangle corresponds to the coefficient of $x^3y^2$ in the expansion of $(x + y)^5$ ?

Row 5, position 2 (from left, starting at position 0): $C(5, 2) = 10$

Row 5, position 3: $C(5, 3) = 10$

Row 5, position 3: $C(5, 3) = 10$ — these are the same, since $C(5,2) = C(5,3) = 10$

Row 3, position 2: $C(3, 2) = 3$