Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To factor the expression [tex]\( 4m^6 - 16p^{10} \)[/tex], we'll follow a step-by-step approach:
1. Identify Common Factors:
Notice that both terms in the expression [tex]\( 4m^6 - 16p^{10} \)[/tex] have a common factor of 4. Thus, we can factor out this common factor first:
[tex]\[ 4m^6 - 16p^{10} = 4(m^6 - 4p^{10}) \][/tex]
2. Recognize the Difference of Squares:
Next, we look inside the parentheses. Notice that [tex]\( m^6 - 4p^{10} \)[/tex] is a difference of squares. Let's rewrite [tex]\( m^6 \)[/tex] as [tex]\( (m^3)^2 \)[/tex] and [tex]\( 4p^{10} \)[/tex] as [tex]\( (2p^5)^2 \)[/tex]:
[tex]\[ m^6 - 4p^{10} = (m^3)^2 - (2p^5)^2 \][/tex]
3. Apply the Difference of Squares Formula:
The difference of squares formula states that [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex].
Applying this to our expression:
[tex]\[ (m^3)^2 - (2p^5)^2 = (m^3 - 2p^5)(m^3 + 2p^5) \][/tex]
4. Combine Factors:
Substituting this result back into the expression we factored out in step 1:
[tex]\[ 4(m^6 - 4p^{10}) = 4((m^3)^2 - (2p^5)^2) = 4(m^3 - 2p^5)(m^3 + 2p^5) \][/tex]
Thus, the fully factored form of the original expression [tex]\( 4m^6 - 16p^{10} \)[/tex] is:
[tex]\[ 4(m^3 - 2p^5)(m^3 + 2p^5) \][/tex]
1. Identify Common Factors:
Notice that both terms in the expression [tex]\( 4m^6 - 16p^{10} \)[/tex] have a common factor of 4. Thus, we can factor out this common factor first:
[tex]\[ 4m^6 - 16p^{10} = 4(m^6 - 4p^{10}) \][/tex]
2. Recognize the Difference of Squares:
Next, we look inside the parentheses. Notice that [tex]\( m^6 - 4p^{10} \)[/tex] is a difference of squares. Let's rewrite [tex]\( m^6 \)[/tex] as [tex]\( (m^3)^2 \)[/tex] and [tex]\( 4p^{10} \)[/tex] as [tex]\( (2p^5)^2 \)[/tex]:
[tex]\[ m^6 - 4p^{10} = (m^3)^2 - (2p^5)^2 \][/tex]
3. Apply the Difference of Squares Formula:
The difference of squares formula states that [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex].
Applying this to our expression:
[tex]\[ (m^3)^2 - (2p^5)^2 = (m^3 - 2p^5)(m^3 + 2p^5) \][/tex]
4. Combine Factors:
Substituting this result back into the expression we factored out in step 1:
[tex]\[ 4(m^6 - 4p^{10}) = 4((m^3)^2 - (2p^5)^2) = 4(m^3 - 2p^5)(m^3 + 2p^5) \][/tex]
Thus, the fully factored form of the original expression [tex]\( 4m^6 - 16p^{10} \)[/tex] is:
[tex]\[ 4(m^3 - 2p^5)(m^3 + 2p^5) \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.