Class 8 Exam > Class 8 Notes > Worksheets with Solutions for Class 8 > Worksheet: We Distribute, Yet Things Multiply
Worksheet: We Distribute, Yet Things Multiply | Worksheets with Solutions for Class 8 PDF Download
Fill in the blanks
Q1: The distributive property of multiplication over addition is written as: a(b + c) = ______.
Q2: 12(x + 4) = ______ + ______.
Q3: (2x + 7)(x + 3) expands to ______.
Q4: The perimeter of a rectangle with length (3x + 5) and breadth (x + 2) is ______.
Q5: The total number of pencils in (x + 3) boxes, each having (2x + 4) pencils, is ______.
State True or False
Q1: The degree of a constant term is 0
Q2: A school buys (3x + 1) books, each having (x + 2) pages. A student claims the total pages are 3x² + 7x + 1.
Q3: 1 is an algebraic expression
Q4: A fruit seller sells (2x + 5) apples every day for 12 days. He says the total apples are 24x + 60.
Q5: In like terms, the numerical coefficients should also be the same
Answer the following questions
Q1: The volume of a rectangular box where length, breadth, and height are 2a, 4b, 8crespectively.
Q2: Carry out the multiplication of the expressions in each of the following pairs.
(i) p − q, 9pq²
(ii) b² − 16, 5b
Q3: Simplify x(2x−1)+5 and find its value at x=−3
Q4:A shopkeeper sells (x + 4) pens at ₹15 each and (2x + 3) pencils at ₹5 each. Find the total money he earns.
Q5: Add: x(x − y), y(y − z), and z(z − x)
Q6: Multiply: (m² + 3n²) × (2m − n)
Q7: A fruit seller sells (2x + 5) apples every day for 12 days. Each apple costs ₹(x + 2). Find the total cost.
Q8 Simplify the expression and evaluate them as directed:4y(3y - 2) + 5(y + 3) - 12for y = -1
Q9:Add 4x(2x + 3) and 5x2 - 7x + 10.
Q10: Simplify (x2−3x+2)(5x−2)−(3x2+4x−5)(2x−1)
The document Worksheet: We Distribute, Yet Things Multiply | Worksheets with Solutions for Class 8 is a part of the Class 8 Course Worksheets with Solutions for Class 8.
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FAQs on Worksheet: We Distribute, Yet Things Multiply - Worksheets with Solutions for Class 8
| 1. What does the title "We Distribute, Yet Things Multiply" imply in mathematical concepts? |  |
Ans. The title suggests a relationship between distribution and multiplication in mathematics. In algebra, distribution refers to the process of multiplying a single term by two or more terms inside parentheses, while multiplication often leads to an increase in quantity. This concept can be illustrated through the distributive property, which states that a(b + c) = ab + ac.
| 2. How does the distributive property work in solving equations? | |
Ans. The distributive property allows us to simplify expressions and solve equations more easily. When applying this property, you distribute the multiplier to each term inside the parentheses. For example, in the equation 3(x + 4) = 15, you would first distribute to get 3x + 12 = 15. Then, you can isolate x by subtracting 12 from both sides and dividing by 3.
| 3. Can you provide real-life examples where distribution and multiplication are applied? | |
Ans. Yes! One real-life example is budgeting. If you have a monthly budget of $300 for groceries, and you plan to spend the same amount each week, you can express this as 4(x) = 300, where x is the weekly budget. Using the distributive property, you understand how your total weekly spending multiplies over the month. Another example is when calculating the total cost of items, where you distribute the cost of each item to find the total.
| 4. Why is it important to understand the relationship between distribution and multiplication in mathematics? | |
Ans. Understanding this relationship is crucial because it forms the foundation for more advanced mathematical concepts, such as factoring, polynomials, and algebraic expressions. Mastering distribution and multiplication enhances problem-solving skills and allows students to tackle complex equations effectively.
| 5. How can students practice the distributive property effectively? | |
Ans. Students can practice the distributive property by solving various algebraic problems, creating their own problems, and using worksheets that emphasize distribution in multiplication. Utilizing online resources, interactive games, and group activities can also make learning this concept more engaging and effective.
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