Solved on Jan 23, 2024

Simplify the expression $20 x^{2} y - 28 x$ .

STEP 1

Assumptions
1. We are given the expression $20x^{2}y - 28x$ .
2. We are asked to simplify the expression, which typically means factoring it if possible.

STEP 2

Identify the greatest common factor (GCF) of the terms in the expression. The GCF is the highest number and the highest power of any variables that divide evenly into all terms of the expression.

STEP 3

Find the GCF of the numerical coefficients. The numerical coefficients are 20 and 28.
$\text{GCF of 20 and 28} = 4$

STEP 4

Find the GCF of the variable terms. The variable terms are $x^{2}y$ and $x$ . The GCF is the lowest power of the variable that is present in all terms.
$\text{GCF of } x^{2}y \text{ and } x = x$

STEP 5

Combine the results from STEP_3 and STEP_4 to find the overall GCF of the expression.
$\text{Overall GCF} = 4x$

STEP 6

Factor the GCF out of each term in the expression.
$20x^{2}y - 28x = 4x(5xy) - 4x(7)$

STEP 7

Simplify the factored expression by combining the terms inside the parentheses.
$20x^{2}y - 28x = 4x(5xy - 7)$
The expression $20x^{2}y - 28x$ is simplified to $4x(5xy - 7)$ .

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Simplify the expression $20 x^{2} y - 28 x$ .

STEP 1

Assumptions
1. We are given the expression $20x^{2}y - 28x$ .
2. We are asked to simplify the expression, which typically means factoring it if possible.

STEP 2

Identify the greatest common factor (GCF) of the terms in the expression. The GCF is the highest number and the highest power of any variables that divide evenly into all terms of the expression.

STEP 3

Find the GCF of the numerical coefficients. The numerical coefficients are 20 and 28.
$\text{GCF of 20 and 28} = 4$

STEP 4

Find the GCF of the variable terms. The variable terms are $x^{2}y$ and $x$ . The GCF is the lowest power of the variable that is present in all terms.
$\text{GCF of } x^{2}y \text{ and } x = x$

STEP 5

Combine the results from STEP_3 and STEP_4 to find the overall GCF of the expression.
$\text{Overall GCF} = 4x$

STEP 6

Factor the GCF out of each term in the expression.
$20x^{2}y - 28x = 4x(5xy) - 4x(7)$

STEP 7

Simplify the factored expression by combining the terms inside the parentheses.
$20x^{2}y - 28x = 4x(5xy - 7)$
The expression $20x^{2}y - 28x$ is simplified to $4x(5xy - 7)$ .

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Simplify the expression 20x2y−28x20 x^{2} y - 28 x20x2y−28x.

STEP 1

Assumptions1. We are given the expression 20x2y−28x20x^{2}y - 28x20x2y−28x.2. We are asked to simplify the expression, which typically means factoring it if possible.

STEP 2

Identify the greatest common factor (GCF) of the terms in the expression. The GCF is the highest number and the highest power of any variables that divide evenly into all terms of the expression.

STEP 3

Find the GCF of the numerical coefficients. The numerical coefficients are 20 and 28.GCF of 20 and 28=4\text{GCF of 20 and 28} = 4GCF of 20 and 28=4

STEP 4

Find the GCF of the variable terms. The variable terms are x2yx^{2}yx2y and xxx. The GCF is the lowest power of the variable that is present in all terms.GCF of x2y and x=x\text{GCF of } x^{2}y \text{ and } x = xGCF of x2y and x=x

STEP 5

Combine the results from STEP_3 and STEP_4 to find the overall GCF of the expression.Overall GCF=4x\text{Overall GCF} = 4xOverall GCF=4x

STEP 6

Factor the GCF out of each term in the expression.20x2y−28x=4x(5xy)−4x(7)20x^{2}y - 28x = 4x(5xy) - 4x(7)20x2y−28x=4x(5xy)−4x(7)

STEP 7

Simplify the factored expression by combining the terms inside the parentheses.20x2y−28x=4x(5xy−7)20x^{2}y - 28x = 4x(5xy - 7)20x2y−28x=4x(5xy−7)The expression 20x2y−28x20x^{2}y - 28x20x2y−28x is simplified to 4x(5xy−7)4x(5xy - 7)4x(5xy−7).

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Simplify the expression $20 x^{2} y - 28 x$ .

Assumptions
1. We are given the expression $20x^{2}y - 28x$ .
2. We are asked to simplify the expression, which typically means factoring it if possible.

Find the GCF of the numerical coefficients. The numerical coefficients are 20 and 28.
$\text{GCF of 20 and 28} = 4$

Find the GCF of the variable terms. The variable terms are $x^{2}y$ and $x$ . The GCF is the lowest power of the variable that is present in all terms.
$\text{GCF of } x^{2}y \text{ and } x = x$

Combine the results from STEP_3 and STEP_4 to find the overall GCF of the expression.
$\text{Overall GCF} = 4x$

Factor the GCF out of each term in the expression.
$20x^{2}y - 28x = 4x(5xy) - 4x(7)$

Simplify the factored expression by combining the terms inside the parentheses.
$20x^{2}y - 28x = 4x(5xy - 7)$
The expression $20x^{2}y - 28x$ is simplified to $4x(5xy - 7)$ .