Binomial expansion and partial fractions

Use Pascal's triangle to find the expansion of (1+x)³

• 1+2x+x²

• 1+2x+2x²+x³

• 1+3x+3x²+x³

• 1+x³

Use Pascal's triangle to expand (x+2y)³

• x³+3x²y+3xy²+y³

• x³+8y³

• 1+3xy+3x²y²+x³y³

• x³+6x²y+12xy²+8y³

Give the binomial you would use to approximate 99⁵

• (100+1)⁵

• (100-1)⁵

• (99+1)⁵

• (99-1)⁵

Find the first 4 terms in the expansion of (1+2x)¹⁰

• 1+20x+180x²+960x³

• 1+10x+45x²+120x³

• 1+10x+90x²+240x³

• 1+1024x¹⁰

When (1-x)^p is expanded, the co-efficient of x² is 40. Given that p > 40, find the co-efficient of x

• 2

• 4

• 5

(p+qx)ⁿ

When n is negative, what range is the expansion valid for?

• ∣x∣<∣q÷p∣

• ∣x∣>∣p÷q∣

• ∣x∣<∣p÷q∣

• ∣x∣>∣q÷p∣

How is a fraction split into partial fractions when a factor is squared in the denominator, such as (x+3)²

• The factor appears twice in the partial fractions, with a power of 2 and a power of 1

• The factor appears one

• The factor appears twice in the partial fractions with a power of 1

• The factor appears twice with a power of 2

How is Pascal's triangle formed?

• All the numbers in the above row are multiplied to get the number below

• The two numbers above are multiplied to get the number below

• All the numbers in the above row are added to get the number below

• The two numbers above are added to get the number below

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