Question

You are given the expression 30x4y3 − 12x3y.

Answer 1

The common factor of the expression $30x^4y^3-12x^3y$ is $6x^3y$.

In the given question,

The given expression is $30x^4y^3-12x^3y$.

We have to find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable and also explain how you found the common factor.

Then we have to Rewrite the expression using the common factor you found in Part A.

We have to find the common factor of the given equation.

We can find the common factor after common the terms that are same in both term.

The equation is $30x^4y^3-12x^3y$.

We can write the equation as

$30x^4y^3-12x^3y=2\times3\times5\times x\times x\times x\times x\times y\times y\times y-2\times2\times3\timesx\times x\times x\times y$

As we can see in the equation that $2\times 3\times x\times x\times x\times y$ is common from both term.

So the equation should be

$30x^4y^3-12x^3y=2\times 3\times x\times x\times x\times y(5\times x\times y\times y-2)$

We can write it as

$30x^4y^3-12x^3y=2\times 3\times x^{(1+1+1)}\times y(5\times x\times y^{(1+1)}-2)$

$30x^4y^3-12x^3y=6x^3y(5xy^2-2)$

So the common factor of the given expression is $6x^3y$.

Now we rewriting the expression.

Since the common factor is $6x^3y$.

So we can rewrite the expression by multiplying the common factor to $(5xy^2-2)$.

So $6x^3y(5xy^2-2)=6x^3y\times5xy^2-6x^3y\times2$

$6x^3y(5xy^2-2)=6\times5x^{3+1}y^{1+2}-6\times2x^3y$

$6x^3y(5xy^2-2)=30x^4y^3-12x^3y$

Hence, the common factor of the expression $30x^4y^3-12x^3y$ is $6x^3y$.

To learn more about common factor link is here

brainly.com/question/22339912

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