Math / Algebra

QuestionFactor. $128 c^{2}-50$

Studdy Solution

STEP 1

1. The expression $128c^2 - 50$ is a difference of terms.
2. The expression can be factored by recognizing common factors or special patterns like the difference of squares.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the expression.
2. Check if the resulting expression is a difference of squares and factor further if possible.

STEP 3

Identify the greatest common factor (GCF) of the terms $128c^2$ and $50$ .
The GCF of 128 and 50 is 2. Factor out the GCF:
$128c^2 - 50 = 2(64c^2 - 25)$

STEP 4

Recognize that $64c^2 - 25$ is a difference of squares. Recall the difference of squares formula:
$a^2 - b^2 = (a - b)(a + b)$
Here, $64c^2$ is $(8c)^2$ and $25$ is $5^2$ . Apply the difference of squares formula:
$64c^2 - 25 = (8c - 5)(8c + 5)$

STEP 5

Combine the factored terms with the GCF factored out:
$2(64c^2 - 25) = 2(8c - 5)(8c + 5)$
This is the fully factored form of the expression.
The factored expression is:
$\boxed{2(8c - 5)(8c + 5)}$

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QuestionFactor. $128 c^{2}-50$

Studdy Solution

STEP 1

1. The expression $128c^2 - 50$ is a difference of terms.
2. The expression can be factored by recognizing common factors or special patterns like the difference of squares.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the expression.
2. Check if the resulting expression is a difference of squares and factor further if possible.

STEP 3

Identify the greatest common factor (GCF) of the terms $128c^2$ and $50$ .
The GCF of 128 and 50 is 2. Factor out the GCF:
$128c^2 - 50 = 2(64c^2 - 25)$

STEP 4

Recognize that $64c^2 - 25$ is a difference of squares. Recall the difference of squares formula:
$a^2 - b^2 = (a - b)(a + b)$
Here, $64c^2$ is $(8c)^2$ and $25$ is $5^2$ . Apply the difference of squares formula:
$64c^2 - 25 = (8c - 5)(8c + 5)$

STEP 5

Combine the factored terms with the GCF factored out:
$2(64c^2 - 25) = 2(8c - 5)(8c + 5)$
This is the fully factored form of the expression.
The factored expression is:
$\boxed{2(8c - 5)(8c + 5)}$

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QuestionFactor. 128c2−50128 c^{2}-50128c2−50

Studdy Solution

STEP 1

1. The expression 128c2−50128c^2 - 50128c2−50 is a difference of terms.2. The expression can be factored by recognizing common factors or special patterns like the difference of squares.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the expression.2. Check if the resulting expression is a difference of squares and factor further if possible.

STEP 3

Identify the greatest common factor (GCF) of the terms 128c2128c^2128c2 and 505050.The GCF of 128 and 50 is 2. Factor out the GCF:128c2−50=2(64c2−25) 128c^2 - 50 = 2(64c^2 - 25) 128c2−50=2(64c2−25)

STEP 4

STEP 5

Combine the factored terms with the GCF factored out:2(64c2−25)=2(8c−5)(8c+5) 2(64c^2 - 25) = 2(8c - 5)(8c + 5) 2(64c2−25)=2(8c−5)(8c+5)This is the fully factored form of the expression.The factored expression is:2(8c−5)(8c+5) \boxed{2(8c - 5)(8c + 5)} 2(8c−5)(8c+5)​

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QuestionFactor. $128 c^{2}-50$

1. The expression $128c^2 - 50$ is a difference of terms.
2. The expression can be factored by recognizing common factors or special patterns like the difference of squares.

1. Identify and factor out the greatest common factor (GCF) from the expression.
2. Check if the resulting expression is a difference of squares and factor further if possible.

Identify the greatest common factor (GCF) of the terms $128c^2$ and $50$ .
The GCF of 128 and 50 is 2. Factor out the GCF:
$128c^2 - 50 = 2(64c^2 - 25)$

Combine the factored terms with the GCF factored out:
$2(64c^2 - 25) = 2(8c - 5)(8c + 5)$
This is the fully factored form of the expression.
The factored expression is:
$\boxed{2(8c - 5)(8c + 5)}$