Math Problem Statement

a) Find the value of 4x − 6y when x = 3 and y = −2. b) Find the value of 2a^2 + 5b^2 when a = −6 and b = 2.

Solution

Let's solve the two parts of the question:

(a) Find the value of 4x6y4x - 6y when x=3x = 3 and y=2y = -2:

Substitute the values of xx and yy into the expression:

4(3)6(2)=12+12=244(3) - 6(-2) = 12 + 12 = 24

So, the value of 4x6y4x - 6y is 24.


(b) Find the value of 2a2+5b22a^2 + 5b^2 when a=6a = -6 and b=2b = 2:

Substitute the values of aa and bb into the expression:

2(6)2+5(2)2=2(36)+5(4)=72+20=922(-6)^2 + 5(2)^2 = 2(36) + 5(4) = 72 + 20 = 92

So, the value of 2a2+5b22a^2 + 5b^2 is 92.


Would you like more details or have any questions on the steps?

Related Questions:

  1. What happens if the signs of xx and yy change in part (a)?
  2. How would you solve part (b) if both aa and bb were positive?
  3. Can you generalize the expression in part (a) for arbitrary values of xx and yy?
  4. How does the solution to part (b) change if aa or bb is zero?
  5. What if you had to find the value of 4x+6y4x + 6y instead in part (a)?

Tip:

When squaring negative numbers, the result is always positive, as (n)2=n2(-n)^2 = n^2.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Quadratic Expressions
Arithmetic Operations

Formulas

4x - 6y
2a^2 + 5b^2

Theorems

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Suitable Grade Level

Grades 7-9