Math Problem Statement

10x + 3y + Bx - y

Solution

Let's work through the problems in the image step by step:

Problem 1:

The equation given is:

10x+3y+Bxy10x + 3y + Bx - y

The instructions ask to determine: a. Variables
b. Coefficients
c. Constants
d. Factors
e. Terms (Suku-Suku)

a. Variables:

The variables are the letters that represent unknown quantities. In the given equation, the variables are:

  • xx
  • yy
  • BB (assuming B is a constant coefficient)

b. Coefficients:

The coefficients are the numbers multiplying the variables. In this case:

  • For 10x10x, the coefficient is 10.
  • For 3y3y, the coefficient is 3.
  • For BxBx, the coefficient is BB.
  • For y-y, the coefficient is -1 (since no number is explicitly written).

c. Constants:

Constants are numbers or symbols without variables. In this expression, no standalone constant (a number without any variable) is present, unless we assume that BB is a known number.

d. Factors:

Factors are quantities that multiply to form terms. For example:

  • In 10x10x, the factors are 10 and xx.
  • In 3y3y, the factors are 3 and yy.
  • In BxBx, the factors are BB and xx.
  • In y-y, the factors are -1 and yy.

e. Terms (Suku-Suku):

The terms are separated by plus or minus signs. The given expression has 4 terms:

  • 10x10x
  • 3y3y
  • BxBx
  • y-y

Problem 2:

The second problem asks to determine which of the following expressions have like terms ("Suku-Suku Sejenis"). Like terms have the same variables raised to the same powers.

Let's check the given options:

  • a. 4p4p4p - 4p
    These are like terms because both terms involve pp, and they are raised to the same power (1).

  • b. 3x2+2y23x^2 + 2y^2
    These are not like terms because one term involves x2x^2 and the other involves y2y^2, different variables.

  • c. 2xyxy2xy - xy
    These are like terms because both terms involve xyxy, the same combination of variables.

  • d. 8p98p - 9
    These are not like terms because one term involves pp and the other is a constant.

  • e. 14p29p14p^2 - 9p
    These are not like terms because the first term involves p2p^2 and the second term involves pp.

  • f. 7p8p7p - 8p
    These are like terms because both terms involve pp.


Do you want more details or have any other questions? Here are some related questions:

  1. How can you identify variables and coefficients quickly in an expression?
  2. What are some examples of constant terms?
  3. What’s the difference between factors and terms in an algebraic expression?
  4. How do like terms help in simplifying expressions?
  5. Why are coefficients important in solving algebraic equations?

Tip: When simplifying expressions, always combine like terms first to make the equation easier to solve!