Expanding (a + b + c)²
Break the trinomial into a binomial and a single term to expand safely.
Equation
y = (x+2+3)^2 - (x^2 + 2^2 + 3^2 + 0*x*2 + 2*x*3 + 2*2*3)
Graph
Table
| x | y |
|---|---|
| -3 | -12 |
| -2 | -8 |
| -1 | -4 |
| 0 | 0 |
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
What this lesson covers
What you do
You shape the function y = (x+a+b)^2 - (x^2 + a^2 + b^2 + k*x*a + 2*x*b + 2*a*b) and watch the graph answer.
Challenges to clear
- Every pair gets a doubled cross-term: slide k to complete 2xa — difference 0 at x = 1.
- Identity: 0 at x = −2 as well — six terms, no more, no less.
- Square the trinomial (2x + a + b). Set a = 3 and b = 4.
- Every pair still gets a doubled cross-term, but the first term is now 2x — so the x·a term is 2·(2x)·a = 4xa. Slide k until the difference is 0 at x = 1.
Check yourself
Which expression is the correct expansion of (a + b + c)²?
- a² + b² + c² + 2ab + 2bc + 2ca — correct
- a² + b² + c² + ab + bc + ca
- a² + b² + c²
- a³ + b³ + c³ + 3abc
Think about it
- (x+a+b)² has THREE cross-terms: 2xa, 2xb and 2ab. Which coefficient is k standing in for?