Today in Precalculus

• Binomial Theorem• Finding specific terms in a

polynomial expansion• homework

Using Binomial Theorem

(2x2 + 3y)4 =

4C0(2x2)4(3y)0

4C1(2x2)3(3y)1

4C2(2x2)2(3y)2

4C3(2x2)1(3y)3

4C4(2x2)1(3y)4

=(1)16x8(1)

=4(8x6)(3y)

=6(4x4)(9y2)

=4(2x2)(27y3)

=(1)(1)(81y4)

16x8+ 96x6y + 216x4y2 + 216x2y3 + 81y4

Using Binomial Theorem

(x – y2)5 =

5C0(x)5(-y2)0

5C1(x)4(-y2)1

5C2(x)3(-y2)2

5C3(x)2(-y2)3

5C4(x)1(-y2)4

5C5(x)0(-y2)5

=1(x5)(1)

=5x4(-y2)

=10(x3)(y4)

=10(x2)(-y6)

=5(x)(y8)

=(1)(1)(- y10)

x5 - 5x4y2 + 10x3y4 - 10x2y6 + 5xy8- y10

Finding Specific Terms

Find the x6y5 term in the expansion of

(x + 3y)11

11C5(x)6(3y)5

= 462x6(243y5)

=112,266x6y5

Finding Specific Terms

Find the x4y9 term in the expansion of

(x - 2y)13

13C9(x)4(-2y)9

=715x4(-512)y9

=-366,080x4y9

Homework

• Pg 715:13,15,19,21

Binomial Theorem(a + b)n = nC0an + nC1an-1b + nC2an-2b2 + … +

nCn-2a2bn-2 + nCn-1abn-1 + nCnbn

Note: nCr can also be written as

n

r