Let's work through the activity step by step.
Given the algebraic expression: `4x - 2y + 3`.
a. If we double the given expression, every term in the expression is multiplied by 2:
The doubled expression is `2 * (4x - 2y + 3)` which simplifies to `8x - 4y + 6`.
b. The number of terms in the doubled expression:
The original expression has three terms (`4x`, `-2y`, `+3`) and doubling it does not change the number of terms. Thus, the doubled expression also has three terms (`8x`, `-4y`, `+6`).
c. The constant term of the doubled expression:
The constant term in the original expression is `3`. When doubled, the constant term becomes `2 * 3 = 6`.
d. The coefficient of x in the doubled expression:
The coefficient of x in the original expression is `4`. When doubled, the coefficient of x becomes `2 * 4 = 8`.
e. The coefficient of y in the doubled expression:
The coefficient of y in the original expression is `-2`. When doubled, the coefficient of y becomes `2 * (-2) = -4`.
f. The degree of the original expression:
The degree of an algebraic expression is the highest power of the variable in the expression. In `4x - 2y + 3`, the variables x and y are both to the first power, so the degree of the original expression is `1`.
g. The degree of the doubled expression:
The degree of the doubled expression remains the same as that of the original expression because the operation of multiplying by a constant does not change the powers of the variables. Therefore, the degree of the doubled expression is also `1`.
h. Are the degrees of the original and doubled expression the same or different? Explain your answers.
The degrees of the original and doubled expressions are the same. In this case, the expressions are linear (degree 1), and doubling the expression does not alter the degree. Doubling an expression only changes the coefficients, not the powers of the variables, so the highest degree term in the expression remains unchanged.
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