Certainly! Let's simplify the given algebraic expression step-by-step.
The given expression is:
[tex]\[4x + 2y + 3x + 5y\][/tex]
Step 1: Identify and group like terms.
The terms involving [tex]\(x\)[/tex] are [tex]\(4x\)[/tex] and [tex]\(3x\)[/tex].
The terms involving [tex]\(y\)[/tex] are [tex]\(2y\)[/tex] and [tex]\(5y\)[/tex].
Step 2: Combine the coefficients of the like terms.
For the terms involving [tex]\(x\)[/tex]:
[tex]\[4x + 3x\][/tex]
Add the coefficients (4 and 3):
[tex]\[4x + 3x = 7x\][/tex]
For the terms involving [tex]\(y\)[/tex]:
[tex]\[2y + 5y\][/tex]
Add the coefficients (2 and 5):
[tex]\[2y + 5y = 7y\][/tex]
Step 3: Write down the simplified expression by combining the results from the previous steps.
Thus, the simplified algebraic expression is:
[tex]\[7x + 7y\][/tex]
So, the final simplified expression for [tex]\(4x + 2y + 3x + 5y\)[/tex] is:
[tex]\[7x + 7y\][/tex]
