Multiplying Polynomials and Pascal's Triangle

A2 3-3 Polynomial Identities

​

​essential question: How can you use polynomial identities to rewrite expression efficiently?

​With larger exponents, a pattern begins to emerge...

The pattern begins with ​Pascal's Triangle which gives the coefficients of the expanded binomial

​Step 3:

Multiple Choice

Multiply the binomial: (x + 3)³

• x³ + 3x² + 3x + 1

• 27x³ + 27x² + 9x + 1

• x³ + 9x² + 27x + 27

• I don't know

Multiple Choice

In Pascal's Triangle, What row do you look for when the exponent is 4?

• Where 4 is the first digit of the row

• Where 4 is the second digit of the column

• Where 4 is the second digit of the row

• Just guess

Multiple Choice

Multiply the binomial: (x - 2)⁴

• x⁴ - 8x³ + 24x² - 32x + 16

• x⁴ + 8x³ + 24x² + 32x + 16

• x⁴ - 4x³ + 6x² - 4x + 1

• x⁴ + 3x³ + 3x² + x

Multiple Choice

Multiply (x + 3)⁶: Which row am I looking at to find the coefficients?

• 1 6 15 20 15 6 1

• 1 5 10 10 5 1

Multiple Choice

Which row of Pascal's Triangle would you use to expand (x+y)³

• 1

• 1 1

• 1 2 1

• 1 3 3 1

Multiple Choice

Find the 4th term in the expansion of (4x-3)⁵.

• 5760

• 5760x³

• -4320x²

• -4320

Multiple Choice

How many terms are the in the expansion of (a+b)⁵

• 3

• 5

• 6

• 25

• 50

Multiple Choice

Expand: (a + b)²

• a² + ab + b²

• a² + 2ab + b²

• a² - ab + b²

• a² - 2ab + b²

Multiple Choice

How many rows in The Pascal's triangle?

• 7

• 8

• 100

• Infinite

Multiple Choice

Expand: (x+2)⁴

• $$x^4+8x^3+16x^2+24x+16$$  

• $$x^4+8x^3+16x^2+32x+16$$  

• $$x^4+8x^3+24x^2+32x+16$$  

• $$x^4+8x^3+32x^2+24x+16$$  

​Review: