Math ↠ Brackets ↠ Binomial formulas

Binomial formulas

The binomial formulas serve to form the exponentiation of a sum with two numbers. There are three binomial formulas which are held for all rational numbers $a$ and $b$:

  1. Binomial formula: $(a+b)^2=a^2+2ab+b^2$

  2. Binomial formula: $(a-b)^2=a^2-2ab+b^2$

  3. Binomial formula: $(a+b)\cdot(a-b)=a^2-b^2$
i

Hint

If you have a term such as $(4x + 2)^2$, you could turn it into $(4x + 2) \cdot (4x + 2)$ and expand brackets. Yet, it is much easier and faster to apply the binomial formulas. Therefore, you should memorize these.

Examples

1. Binomial formula

$(4x+3)^2$ $=(4x)^2+2\cdot4x\cdot3+3^2$ $=16x^2+24x+9$

2. Binomial formula

$(4x-3)^2$ $=(4x)^2-2\cdot4x\cdot3+3^2$ $=16x^2-24x+9$

3. Binomial formula

$(4x+3)\cdot(4x-3)$ $=(4x)^2-3^2$ $=16x^2-9$


!

Remember

The binomial formulas can also be applied backwards.

Example

The second binomial formula applied backwards:
$4x^2-24x+36=(2x-6)^2$