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Cogito

Integrated Math 3 · Chapter 1 · Lesson 3

Practice Worksheet

Polynomial Identities and the Binomial Theorem

Expanding without multiplying it all out.

12 problems · about 21 minutes · A-APR.C.4, A-APR.C.5

NameDate

Figure — use these to answer the problems

Row 4 of the triangle: 1, 4, 6, 4, 1. The coefficients rise to a peak 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

How many terms does (a + b)⁸ have?
Answer
2
Where do the binomial coefficients come from?
- Combinations: choosing which factors contribute a b.
- They are memorised with no reason.
How many terms in (a + b)⁹?
Answer
What is 6C2?
Answer
In (a + b)⁴, coefficient of a²b²?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

In (a + b)², what is the coefficient of ab?
Answer
Sum of row 3 of the triangle: 1, 3, 3, 1?
Answer
In (a + b)⁷, the exponents of every term total what?
Answer

Stretch Yourself

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

4 problems

9
Match each expression with its factorisation.
Draw a line from each item on the left to its match on the right.
- a squared minus b squared
- a cubed minus b cubed
- a cubed plus b cubed
- (a minus b)(a plus b)
- (a minus b)(a squared plus ab plus b squared)
- (a plus b)(a squared minus ab plus b squared)
In (a + b)⁶, coefficient of a⁵b?
Answer
The Terms
How many terms does (a + b)⁶ have?
Answer
The Coefficient
In (a + b)⁵, what is the coefficient of a³b²?
Answer