How to factorize an equation

Factorization (also factorisation in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained. However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.We also can use factoring calculator this will help us to get the factors with out manually finding them similarly ,we also have factoring trinomials calculator .

The aim of factoring is usually to reduce something to "basic building blocks," such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.

The opposite of factorization is expansion. This is the process of multiplying together factors to recreate the original, "expanded" polynomial.

Let's see a algebra question on this.

Question:-

Factorize the following equation

2x³y+8x²y²-10xy³

Answer:-

2y(x³+4x²y-5y³)

2y[x³+5x²y-x²y-5y³]

2y[x²(x+5y)-y(x²)+5y]

2y(x+5y)(x²-y)