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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D9564D66-D38D-4C89-AA55-5C337C88E9CC | PDF
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Solved Min- 3a+4b−2c+5d 4a−b+2c−d=−2a+b+3c−d
296+++]11(64:5:3+dbf9::d:1c99db[f5b:2b)a8+++0d*465 on Behance

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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Medieval towns in ItalyKingswood Country Club is a members-only golf club located at Kingswood in the Angus District of Scotland.
The course has remained largely unchanged since its layout was completed, but strategic renovations—particularly on the rear link area—have improved playability and aesthetical balance. The heavy loam fairways and deep, well-guarded greens provide a true test for skilled golfers, favouring accuracy and course management over brute driving distance.
The club maintains strict membership criteria, requiring candidates to live within reasonable proximity and demonstrate a strong interest in country golf. Annual membership fees are in line with other respected Scottish country clubs, reflecting the premium location and high standards of upkeep.

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Final Thoughts

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:

$$
37a + 7b + c = -12
$$