Question
(b) \( (\sqrt{x}+2 \sqrt{x})+(3 \sqrt{x}+4 \sqrt{x}) \) (c) \( (3 a+7 b-9)-(5 a+9 b+21) \)
Ask by Cox Mcdonald. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(b) \( 10\sqrt{x} \)
(c) \( -2a - 2b - 30 \)
Solution
Let's simplify each expression step by step.
For (b):
(√x + 2√x) + (3√x + 4√x)
Step 1: Combine like terms in each set of parentheses.
√x + 2√x = (1 + 2)√x = 3√x
3√x + 4√x = (3 + 4)√x = 7√x
Step 2: Now add the results:
3√x + 7√x = (3 + 7)√x = 10√x
So, (b) simplifies to 10√x.
For (c):
(3a + 7b - 9) - (5a + 9b + 21)
Step 1: Distribute the subtraction (change the signs of all terms in the second parentheses):
= 3a + 7b - 9 - 5a - 9b - 21
Step 2: Combine like terms:
For a: 3a - 5a = -2a
For b: 7b - 9b = -2b
For constants: -9 - 21 = -30
Thus, (c) simplifies to -2a - 2b - 30.
These are your simplified expressions.
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Simplify this solution Beyond the Answer
Combining like terms can be as satisfying as piecing together a puzzle! For the first expression \( (\sqrt{x}+2 \sqrt{x})+(3 \sqrt{x}+4 \sqrt{x}) \), gather all the square root terms: \( (1 + 2 + 3 + 4) \sqrt{x} = 10 \sqrt{x} \). Then we have the second expression \( (3 a+7 b-9)-(5 a+9 b+21) \). Distributing the negative sign gives us \( 3a + 7b - 9 - 5a - 9b - 21 \). Combining the like terms leads to \( (3 - 5)a + (7 - 9)b + (-9 - 21) = -2a - 2b - 30 \). Voila! Simplifying equations is a fun adventure!
