Chapter 6, Problem 1RP

To determine

The factor form of the given expression by factoring out the greatest common factor.

Answer to Problem 1RP

Solution:The complete factor of the expression $12x^3-20x^{2}y$ is $4x^2\left(3x-5y\right)$ .

Explanation of Solution

Given:The given expression is $12x^3-20x^{2}y$ .

Calculation:

To factor an expression, we look for the greatest common numerical factor that divides all coefficients of all the terms. Then check for the greatest common variable factor; look for the largest common exponent which is common to all the terms.

The greatest common numerical factor in $12x^3-20x^{2}y$ is 4.

Also, the greatest common variable factor in $12x^3-20x^{2}y$ is $x^2$ .

Now, factorize the expression separating highest common factor. The greatest common factor $12x^3-20x^{2}y$ is $4x^2$ .

  $\begin{array}{c}12x^3-20x^{2}y\\ =4\times 3x^3-4\times 5x^{2}y\left[\text{Common}\text{factor}4\right]\\ =4\left(3x^3-5x^{2}y\right)\\ =4\left(3\times x^2\times x-5\times x^2\times y\right)\left[\text{Common}\text{factor}{x}^2\right]\\ =4x^2\left(3\times x-5\times y\right)\end{array}$

Further the above expression is

  $4x^2\left(3\times x-5\times y\right)=4x^2\left(3x-5y\right)$ .

The complete factor of the expression $12x^3-20x^{2}y$ is $4x^2\left(3x-5y\right)$ .

Conclusion:

Thus, the complete factor of the expression $12x^3-20x^{2}y$ is $4x^2\left(3x-5y\right)$ .