$ (64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -7 - 5 $ - Imagemakers
Understanding the Equation: $ (64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -7 - 5 $
Understanding the Equation: $ (64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -7 - 5 $
When tackling algebraic expressions, simplifying and analyzing equations plays a crucial role in both academic learning and real-world applications. In this article, we break down the expression:
$$
(64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -7 - 5
$$
Understanding the Context
and solve it step-by-step to reveal its hidden value and meaning.
Step 1: Simplify the Left-Hand Side (LHS)
We begin by simplifying the expression using the distributive property:
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Key Insights
$$
(64a + 16b + 4c + d) - (27a + 9b + 3c + d)
$$
Distribute the minus sign across the second parentheses:
$$
64a + 16b + 4c + d - 27a - 9b - 3c - d
$$
Now combine like terms:
- $a$-terms: $64a - 27a = 37a$
- $b$-terms: $16b - 9b = 7b$
- $c$-terms: $4c - 3c = 1c = c$
- $d$-terms: $d - d = 0$
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So the simplified LHS becomes:
$$
37a + 7b + c
$$
Step 2: Simplify the Right-Hand Side (RHS)
The right-hand side is:
$$
-7 - 5 = -12
$$
Step 3: Set Up the Equation
Now the equation reads:
$$
37a + 7b + c = -12
$$
