See the binomial square formula as area, and run it backward — that's factoring
Split (a+b)² apart as the area of a square, and it's visually obvious why the formula looks the way it does. Factoring then runs that same formula in reverse, which is exactly how you find the two roots of a quadratic equation.
(a+b)² = a² + 2ab + b² isn't a formula you have to memorize — it's a visible fact: a square with side length (a+b), split into four pieces by a and b, has an area equal to the sum of those four pieces.
Factoring runs this same formula backward. Regroup a multi-term expression like x²+5x+6 into multiplied form, x²+5x+6 = (x+2)(x+3), and the quadratic equation x²+5x+6=0 turns into (x+2)(x+3)=0 — making the two roots, x=−2 or x=−3, easy to find.
Change a and b with the sliders to see the area behind why (a+b)² becomes that formula, then try guessing the two roots of a quadratic equation yourself using factoring.
The binomial square formula (a+b)² = a² + 2ab + b² is exactly the same as computing the area of a square with side length (a+b) as the sum of four pieces split by a and b.
a3
b2
Factoring runs the binomial formula backward. If you can split an expression of the form x² + bx + c into (x−r₁)(x−r₂), then the two roots of x² + bx + c = 0 are exactly r₁ and r₂ — because for a product to equal 0, one of the two factors must be 0.
Question 1/10 · 0 correct
Answer correctly or press "show solution" to see the factoring steps.
The coefficient c is the two roots multiplied together, and b is the two roots added together with the sign flipped. Use this relationship in reverse to guess the two roots.