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BARSIC [14]
2 years ago
12

Identify the GCF of 10x4y3 − 5x3y2 + 20x2y.

Mathematics
2 answers:
viktelen [127]2 years ago
8 0
<h2>Answer:</h2>

The GCF of the given expression is:

                          5x^2y

<h2>Step-by-step explanation:</h2>

The GCF ( greatest common factor ) is the greatest divisor which divides all the terms completely.

Here we have the expression as:

10x^4y^3-5x^3y^2+20x^2y

Here we see that the factors of the first term are:

10x^4y^3=2\times 5\times x\times x\times x\times x\times y\times y\times y

The factor of the second term is:

-5x^3y^2=-1\times 5\times x\times x\times x\times y\times y

and the factor of the third term is:

20x^2y=2\times 2\times 5\times x\times x\times y

i.e. the factor which is common to all the three terms are:

5\times x\times x\times y=5x^2y

Hence, the GCF is:   5x^2y

Agata [3.3K]2 years ago
7 0
The GCF, or greatest common factor, is the greatest positive integer that evenly multiplies to make the numbers in the set. For simple numbers, GCF(12, 80, 44) is 4.

The strategy for expressions with variables is still to factor out the greatest term.

For 10x^4y^3-5x^3y^2+20x^2y, we look for the largest factor in each term.

For 10x^4y^3, the largest factors are x^4 and y^3. We'll come back to the coefficients in a minute.

For -5x^3y^2, the largest factors are x^3 and y^2. Now, looking back to the previous term and also considering the coefficients, the largest factor of the two is 5x^3y^2. You could rewrite the first term as (5x^3y^2)(2xy) and the second term as -1(5x^3y^2).

Now, we consider the last term, 20x^2y. The largest factor common to the two other terms is 5x^2y.

And that's our final answer for the GCF (answer D).
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