A quadratic expression has form ax2+bx+c, where a 0. Expand a product by multiplying every term in one bracket by every term in the other, then collect like terms. **Identity** | **Useful structure** (a+b)2=a2+2ab+b2 | Square of a sum (a-b)2=a2-2ab+b2 | Square of a difference a2-b2=(a+b)(a-b) | Difference of two squares Example (2x-3)(x+4)=2x2+8x-3x-12 =2x2+5x-12. Using the square identity, (2x-3)2=4x2-12x+9. The middle term is essential: squaring a sum does not mean squaring only its separate terms.

A quadratic expression has form \(ax^2+bx+c\), where \(a\ne0\). Expand a product by multiplying every term in one bracket by every term in the other, then collect like terms.

\(\begin{aligned}(2x-3)(x+4)&=2x^2+8x-3x-12\\&=2x^2+5x-12.\end{aligned}\)

Using the square identity, \((2x-3)^2=4x^2-12x+9\). The middle term is essential: squaring a sum does not mean squaring only its separate terms.

Identity	Useful structure
\((a+b)^2=a^2+2ab+b^2\)	Square of a sum
\((a-b)^2=a^2-2ab+b^2\)	Square of a difference
\(a^2-b^2=(a+b)(a-b)\)	Difference of two squares

Expansion and the three identities

Expansion and the three identities