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Cogito

Precalculus · Chapter 4 · Lesson 2

Practice Worksheet

The Binomial Theorem

Expand a power without multiplying it out.

12 problems · about 22 minutes · TEKS P.5.F

NameDate

Figure — use these to answer the problems

Row 4 of Pascal’s triangle: 1, 4, 6, 4, 1. The coefficients rise to a peak in the middle and fall back symmetrically.
4C01
4C14
4C26
4C34
4C01
4C14
4C26
4C34
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. How many terms does (x + y)⁸ have?

    Answer

  2. Where do the binomial coefficients come from?

    • Combinations: choosing which factors contribute a y.
    • They are memorised values with no reason behind them.

  3. How many terms in (x + y)⁹?

    Answer

  4. What is 6C2?

    Answer

  5. In (x + y)⁴, what is the coefficient of x²y²?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. What is the sum of row 3 of Pascal’s triangle: 1, 3, 3, 1?

    Answer

  2. In (x + y)⁷, the exponents of every term total what number?

    Answer

  3. In (x + y)⁶, what is the coefficient of x⁵y?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put row 5 of Pascal’s triangle in order, left to right.

    Write 1 to 4 in the boxes to put these in order.

    • 1
    • 5
    • 10
    • 10 again

  2. In (x − y)³, what is the sign of the y³ term? Enter 1 for positive, 2 for negative.

    Answer

  3. The Row

    How many terms does the expansion of (x + y)⁶ have?

    Answer

  4. The Coefficient

    In (x + y)⁵, what is the coefficient of x³y²?

    Answer