Question
64x^3y-32xy^4+40xy^2
Answers
Answered by
GPT-4o mini
To simplify the expression \(64x^3y - 32xy^4 + 40xy^2\), we can factor out the greatest common factor (GCF) from all the terms.
1. Identify the GCF:
- The coefficients are \(64\), \(-32\), and \(40\). The GCF of these numbers is \(8\).
- The variable parts include \(x\) and \(y\). The lowest powers of \(x\) and \(y\) present in all terms are \(x^1\) and \(y^1\). Thus, the GCF is \(8xy\).
2. Factor out \(8xy\):
\[
64x^3y \div 8xy = 8x^2
\]
\[
-32xy^4 \div 8xy = -4y^3
\]
\[
40xy^2 \div 8xy = 5y
\]
3. Write the expression with the GCF factored out:
\[
64x^3y - 32xy^4 + 40xy^2 = 8xy(8x^2 - 4y^3 + 5y)
\]
Therefore, the expression can be simplified to:
\[
8xy(8x^2 - 4y^3 + 5y)
\]
1. Identify the GCF:
- The coefficients are \(64\), \(-32\), and \(40\). The GCF of these numbers is \(8\).
- The variable parts include \(x\) and \(y\). The lowest powers of \(x\) and \(y\) present in all terms are \(x^1\) and \(y^1\). Thus, the GCF is \(8xy\).
2. Factor out \(8xy\):
\[
64x^3y \div 8xy = 8x^2
\]
\[
-32xy^4 \div 8xy = -4y^3
\]
\[
40xy^2 \div 8xy = 5y
\]
3. Write the expression with the GCF factored out:
\[
64x^3y - 32xy^4 + 40xy^2 = 8xy(8x^2 - 4y^3 + 5y)
\]
Therefore, the expression can be simplified to:
\[
8xy(8x^2 - 4y^3 + 5y)
\]