# Factoring Problems and Solutions

There are five fundamental concepts to factorize the expressions in mathematics. You have learned the methods of factorizing the expressions and the following are the list of problems on each factorisation method with understandable steps of solutions to learn how to use the factorization method to factorise the expressions mathematically.

### Taking out the Common factor

$(1).\,\,\,$ $4x^2y^3-6x^3y^2-12xy^2$

$(2).\,\,\,$ $36(x+y)^3-54(x+y)^2$

$(3).\,\,\,$ $2x^5y+8x^3y^2-12x^2y^3$

List of the problems on factoring the solutions to learn how to factorise the expressions by taking out the common factors.

### Factoring by Grouping

$(1).\,\,\,$ $9x^3+6x^2y^2-4y^3-6xy$

$(2).\,\,\,$ $36(x+y)^3-54(x+y)^2$

$(3).\,\,\,$ $\dfrac{1}{25x^2}+16x^2+\dfrac{8}{5}-12x-\dfrac{3}{5x}$

List of the questions on factorizing the solutions to learn how to factorize the expressions by grouping.

### Splitting the Middle term

$(1).\,\,\,$ $2x^2y^2-7xy-30$

$(2).\,\,\,$ $5(3x+y)^2+6(3x+y)-8$

$(3).\,\,\,$ $2x^2+\dfrac{x}{6}-1$

List of the questions with solutions to learn how to factorise the expressions by splitting the middle term.

### Difference of the squares

$(1).\,\,\,$ $x^2-16$

$(2).\,\,\,$ $x^4+x^2+1$

$(3).\,\,\,$ $8xy^2-18x^3$

List of the problems on factorising the expressions by the difference of the squares.

### Difference of the cubes

$(1).\,\,\,$ $64x^3+1$

$(2).\,\,\,$ $x^3-\dfrac{1}{x^3}-2x+\dfrac{2}{x}$

$(3).\,\,\,$ $8x^3+12x^2+6x+1-27y^3$

List of the problems on factoring the expressions by the difference of the cubes.

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