Math Expression Factorization

Factorizing is the action of transforming a sum into a product (a multiplication) of 2 factors (or more).

Factorization by finding a common factor

Example: \( 2a + 2b \) has the common factor \( 2 \), so \( 2a + 2b = 2(a+b) \)

Factorization by identifying a remarkable identity

The most common outstanding identities are \( (a+b)^2 = a^2 + 2ab + b^2 \), \( (a-b)^2 = a^2 - 2ab + b^2 \) or \( (a+b)(a-b)=a^2 - b^2\)

Example: \(x^2 + 2x-a^2 + 1 \) is a remarkable identity \(a^2 + 2ab + b^2 = (a+b)^2 \) so \( x^2 + 2x - a^2 + 1 = (-a+x+1)(a+x+1) \)

dCode can factorize a mathematical expression in order to express it as a product of factors. dCode knows how to recognize a remarkable identity and manages unknowns and variables thanks to its formal calculator.

dCode factorizes trigonometric expression in order to simplify them by expressing them with sin and cos

Example: $$ 1+1/\sec(x) = 2\cos(x/2)^2 $$

Example: $$ \cos(x+y) + \sin(x)\sin(y) = \cos(x)\cos(y) $$

The solver/factorizer has no real steps, at least not steps similar to those required of college or high school. For the moment steps are not displayed, but the solver allows checking a result.