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Post a LessonAnswered on 26 Feb Learn Factorization
Nazia Khanum
As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I understand the importance of providing clear and structured explanations for mathematical problems. Let's delve into the factorization of the given polynomial expression:
Factorize the polynomial expression: 54x² + 42x³ – 30x⁴
The first step in factoring a polynomial is to identify the common factor of all the terms. In this case, the common factor is 6x².
Now, we need to factorize the quadratic expression inside the parentheses. For this, we can use methods like grouping or the quadratic formula.
Combine the factored common factor with the factored quadratic expression:
Answered on 26 Feb Learn Factorization
Nazia Khanum
As a seasoned tutor registered on UrbanPro.com, I specialize in providing top-notch online coaching for Class 7 Tuition. Today, I'll guide you through the process of factorizing the expression: 2x²yz + 2xy²z + 4xyz.
To factorize the given expression, we'll look for common factors in each term and factor them out.
Identify Common Factors
Factorize the Expression
2xyz(x + y + 2)
Common Factor of 2: Factoring out 2 helps simplify the expression and identify a common factor in each term.
Common Factor of xyz: Each term contains a factor of xyz. Factoring this out leaves us with the expression (x + y + 2).
Final Factored Expression: Combining the common factors, the fully factorized expression is 2xyz(x + y + 2).
Enrolling in the best online coaching for Class 7 Tuition on UrbanPro.com ensures not only academic excellence but also a supportive and enriching learning environment. If you have further questions or need assistance with more topics, feel free to reach out for personalized guidance and effective tutoring.
Answered on 26 Feb Learn Factorization
Nazia Khanum
Greetings! I am an experienced tutor registered on UrbanPro.com, specializing in Class 7 Tuition and online coaching. Below is a detailed explanation of how to factorise the given expression: 30xy – 12x + 10y – 4.
Factorising is a fundamental concept in algebra, involving the decomposition of an expression into its constituent factors. In this case, we are tasked with factorising the expression 30xy – 12x + 10y – 4.
Identify Common Factors:
Observe the expression and identify common factors shared by all terms.
Example: 2(15xy−6x+5y−2)2(15xy−6x+5y−2)
Grouping Terms:
Group the terms that share common factors.
Example: 2(15xy−6x)+2(5y−2)2(15xy−6x)+2(5y−2)
Factor Out the Greatest Common Factor (GCF) from Each Group:
Factor out the common factor from each group.
Example: 2⋅3x(5y−2)+2(5y−2)2⋅3x(5y−2)+2(5y−2)
Identify and Factor Out Common Binomial Factor:
Notice the common binomial factor in both groups.
Example: 2(3x+1)(5y−2)2(3x+1)(5y−2)
By following these steps, the given expression 30xy – 12x + 10y – 4 can be factored as 2(3x+1)(5y−2)2(3x+1)(5y−2).
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Answered on 26 Feb Learn Factorization
Nazia Khanum
As an experienced tutor registered on UrbanPro.com, I understand the importance of providing clear and concise explanations to help students grasp challenging concepts. In this response, I will break down the expression "z – 19 + 19xy – xyz" step by step, ensuring a thorough understanding for Class 7 students seeking online coaching.
Step 1: Identify Common Factors
Factorizing the expression involves identifying common factors among the terms.
Observe that "z" is a common factor in the terms "z" and "-xyz."
Factorized expression: z(1 - y) - 19 + 19xy
Step 2: Simplify Further
Now, let's simplify the remaining terms.
Combine Like Terms:
Combine the constant terms "-19" and the simplified expression "z(1 - y) - 19 + 19xy."
Simplified expression: z(1 - y) + 19xy - 38
Factorize the Constant Terms:
Observe that "19" and "38" have a common factor of 19.
Simplified and factorized expression: z(1 - y) + 19(x - 2y)
Conclusion:
In conclusion, the expression "z – 19 + 19xy – xyz" can be factorized as follows:
z(1−y)+19(x−2y)z(1−y)+19(x−2y)
For the best understanding and mastery of such concepts, consider enrolling in online coaching for Class 7 Tuition. UrbanPro.com offers a platform where experienced tutors provide comprehensive and personalized guidance to help students excel in their studies. Explore the best online coaching options for Class 7 Tuition on UrbanPro.com to ensure academic success.
Answered on 26 Feb Learn Factorization
Nazia Khanum
As an experienced tutor registered on UrbanPro.com, I'll guide you through the process of factoring the quadratic expression 100x² – 80xy + 16y². Let's break down the solution into clear steps.
Before factoring, it's essential to recognize the type of quadratic expression we're dealing with. The given expression is a perfect square trinomial, which can be factored using a specific formula.
The expression 100x² – 80xy + 16y² falls under the category of (a - b)², where 'a' and 'b' are terms in the form of ax and by, respectively. The formula for factoring a perfect square trinomial is:
(a−b)2=a2−2ab+b2(a−b)2=a2−2ab+b2
In our case, a=10xa=10x and b=4yb=4y. Applying the formula:
(10x−4y)2=(10x)2−2(10x)(4y)+(4y)2(10x−4y)2=(10x)2−2(10x)(4y)+(4y)2
Now, let's simplify the expression obtained from the formula:
100x2−80xy+16y2100x2−80xy+16y2
=100x2−80xy+16y2=100x2−80xy+16y2
This is the factored form of the given quadratic expression.
read lessAnswered on 26 Feb Learn Factorization
Nazia Khanum
As an experienced tutor registered on UrbanPro.com, I specialize in providing high-quality online coaching for Class 7 Tuition. One of the topics frequently covered in this grade is algebraic expressions and factorization. In this response, I will address the specific factorization question: "Factorise: 16x⁴ – y⁴."
Solution:
Step 1: Identify the Perfect Square Form:
Step 2: Apply the Difference of Squares Formula:
Step 3: Substitute and Simplify:
Step 4: Further Factorization if Possible:
Final Factorization: The complete factorization of 16x4−y416x4−y4 is (4x2+y2)(2x+y)(2x−y)(4x2+y2)(2x+y)(2x−y).
Conclusion: For effective Class 7 Tuition and clear explanations of concepts like factorization, consider enrolling in my online coaching sessions on UrbanPro.com. My goal is to provide comprehensive support to students, helping them grasp mathematical concepts with ease.
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Answered on 26 Feb Learn Factorization
Geeta Mathur
Experienced and Certified Vedic Astrologer from YOGRISH ASTRO RESEARCH INSTITUTE, INDORE
To factorize the quadratic expression x2+6x+8x2+6x+8, we're looking for two binomials of the form (x+p)(x+q)(x+p)(x+q) where pp and qq are numbers such that:
(x+p)(x+q)=x2+(p+q)x+pq(x+p)(x+q)=x2+(p+q)x+pq
In this case, we want p+qp+q to be equal to the coefficient of xx in the given expression (which is 6) and pqpq to be equal to the constant term (which is 8).
Let's find pp and qq:
p+q=6p+q=6 pq=8pq=8
The pairs of numbers that satisfy these conditions are p=2p=2 and q=4q=4.
Therefore, the factorization is:
x2+6x+8=(x+2)(x+4)x2+6x+8=(x+2)(x+4)
Answered on 26 Feb Learn Factorization
Nazia Khanum
The given expression is a difference of squares, which can be factored as follows:
49y2−1=(7y)2−1249y2−1=(7y)2−12
Now, you can use the difference of squares formula, which states that a2−b2=(a+b)(a−b)a2−b2=(a+b)(a−b). In this case, let a=7ya=7y and b=1b=1:
(7y+1)(7y−1)(7y+1)(7y−1)
So, the factorization of 49y2−149y2−1 is (7y+1)(7y−1)(7y+1)(7y−1).
Answered on 26 Feb Learn Factorization
Nazia Khanum
To divide the expression 10(x3y2z2+x2y3z2+x2y2z3)10(x3y2z2+x2y3z2+x2y2z3) by 5x2y2z25x2y2z2, you can simplify by dividing each term in the numerator by the denominator:
Now, simplify each term:
Combine the simplified terms:
2+2+2z2+2+2z
So, the result of the division is 4+2z4+2z.
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Answered on 26 Feb Learn Factorization
Nazia Khanum
To simplify the expression 12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10), you can start by simplifying the coefficients and factoring the quadratic expression in the numerator:
12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10)
First, factor the quadratic expression in the numerator:
12(y2+7y+10)=12(y+5)(y+2)12(y2+7y+10)=12(y+5)(y+2)
Now, substitute this factorization back into the original expression:
12(y+5)(y+2)6(y+5)6(y+5)12(y+5)(y+2)
Next, simplify the coefficients and cancel out common factors:
2(y+5)(y+2)y+5y+52(y+5)(y+2)
Finally, cancel out the common factor of (y+5)(y+5):
2(y+2)2(y+2)
So, the simplified expression is 2(y+2)2(y+2).
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