Thus, 200l + 160w + 50lw is the algebraic expression for the total cost.
1. Can you identify the terms, variables and coefficients of this algebraic expression?
2. How is it different from the algebraic expression 4x + 5y + 3 for Raju’s pens and pencils?
- 1. Can you identify the terms, variables and coefficients of this algebraic expression?
- 2. How is it different from the algebraic expression 4x + 5y + 3 for Raju’s pens and pencils?
Step-by-step solution
Idea: A term is a part joined to the others by + or −. The variables are the letters. The coefficient is the number multiplying the variable part of a term. A constant is a term with no variable.
1. Can you identify the terms, variables and coefficients of this algebraic expression?
- Split at the + signs: the terms are 200l, 160w and 50lw.½ mark
- The letters used are l (length) and w (width), so the variables are l and w.½ mark
- Coefficients: 200 is the coefficient of l, 160 is the coefficient of w, and 50 is the coefficient of lw.½ mark
2. How is it different from the algebraic expression 4x + 5y + 3 for Raju’s pens and pencils?
- Same: both expressions use two variables.½ mark
- Different 1: 200l + 160w + 50lw has a term 50lw in which the two variables are multiplied together (it came from the area l × w). In 4x + 5y + 3 every term has at most one variable.½ mark
- Different 2: 4x + 5y + 3 has a constant term, 3 (the free pens). The cost expression has no constant term: every part of the cost depends on l or w.½ mark
Answer to write in the exam
1.
Terms: 200l, 160w, 50lw
Variables: l, w
Coefficients: 200 (of l), 160 (of w), 50 (of lw)
2.
Both expressions have two variables.
200l + 160w + 50lw has a product term 50lw; 4x + 5y + 3 has no product term.
4x + 5y + 3 has a constant term 3; 200l + 160w + 50lw has no constant term.
Common mistakes that cost marks
- Saying the coefficient of 50lw is 50l (or that it has no coefficient). The coefficient is the number, 50; the variable part is lw.
- Listing lw as a third variable. lw is a product of the two variables l and w, not a new variable.
- Calling 3 in 4x + 5y + 3 a coefficient. It has no variable attached, so it is a constant term.
How this can come in the exam
In the expression 7pq + 3p − 2, the coefficient of pq is
- 7
- 3
- −2
- 7p
Show answer
(A) 7
The number multiplying pq is 7.
Assertion (A): The expression 5m + 8n + 2mn has no constant term.
Reason (R): Every term of 5m + 8n + 2mn contains at least one variable.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(A) Both A and R are true, and R is the correct explanation of A.
A constant term is a term with no variable. Each term has a variable, so there is no constant term: R explains A.
Try one yourself
Write the terms, variables and coefficients of 12a + 9ab − 4b + 6, and say which term is the constant.
Show answer
Terms: 12a, 9ab, −4b, 6. Variables: a, b. Coefficients: 12 (of a), 9 (of ab), −4 (of b). Constant: 6.
More questions like this
- A wire of length 20 cm is bent in different ways to form rectangles. For example, we can have a rectangle with length 7 cm and width 3 cm. We can also have one of length 5.5 cm and width 4.5 cm. (Think of a few more ways of forming such rectangles.) Can you write an expression for the area of such rectangles?
- The expression for the area of these rectangles is x(10 − x) or 10x − x2.
1. Can you identify the terms, variables and coefficients of this algebraic expression?
2. Can you point out any similarity or difference between the algebraic expressions obtained for Raju’s pens and pencils (4x + 5y + 3) and for these rectangles? - Find the degrees of the following polynomials:
- Write polynomials of degrees 1, 2 and 3.
- What are the coefficients of x2 and x3 in the polynomial x4 − 3x3 + 6x2 − 2x + 7?