Functions site presentation

Combination in Polynomials

What is Combination?

• Using more than one technique (e.g. Square of binomial, difference of squares, distributive property) in sequence
• Like using the FOIL method and then combining like terms afterward
• Or applying the square formula and then the distributive property

Why It Matters & How to Use It

• Most homework and test questions require multiple steps
  1. Look for patterns you recognise (squares, products)
  2. Solve each part separately using the right formula
  3. Plug those answers back into the original problem
  4. Simplify by combining like terms

Example Walkthrough

1. Break it into parts you know

For the squared term:

• $(3-4x{)}^2=3^2-2(3)(4x)+(4x{)}^2=9-24x+16x^2$

For the product term:

• $(5-2x)(5+2x)=5^2-(2x{)}^2=25-4x^2$

2. Distribute the term throughout the bracket

• $-5(9-24x+16x^2)=-45+120x-80x^2$
• $3(25-4x^2)=75-12x^2$

3. Add everything together

• $-45+120x-80x^2+75-12x^2$
• $=30+120x-92x^2$
• Written with highest power first: $-92x^2+120x+30$ or $92x^2-120x-30$