\cdot (4 + b) = 4^2 + 12 \Rightarrow 4(4 + b) = 16 + 12 = 28

Understanding the Equation: 4 + b = 4² + 12, Simplified to 4(4 + b) = 28 – A Step-by-Step Explanation

Solving equations step-by-step is a foundational skill in algebra, and mastering them boosts confidence in working with variables. One common challenge is simplifying expressions on both sides of an equation. This article breaks down the logical progression from the initial equation to its final simplified form:
(4 + b) = 4² + 12 → 4(4 + b) = 28

Understanding the Context

Step 1: Start with the Given Equation

We begin with:
4 + b = 4² + 12

The goal is to simplify the right-hand side and solve for variable b. First, evaluate any powers and constants.

$\cdot (4 + b) = 4^2 + 12 \Rightarrow 4(4 + b) = 16 + 12 = 28$

Key Insights

Step 2: Evaluate the Right-Hand Side

Calculate 4² + 12:
4² = 16
So,
4² + 12 = 16 + 12 = 28

Now, replace the right-hand side:
4 + b = 28

This equation is valid but doesn’t isolate b in a simplified form involving a factored expression. To advance, we need to rewrite the equation using distributive property.

🔗 Related Articles You Might Like:

📰 Silver Prices 📰 Ukkolanvaara Gold Deposit 📰 Cliffs Stock 📰 26250 629890 📰 Serious Fun Unlocked The Best Party Games For Adults That Drive Everyone Wild 1009719 📰 Width Frac253 M Length Frac653 M1 A Rectangular Garden Is 15 Meters Long And 10 Meters Wide If A Path Of Uniform Width Is Built Inside The Garden Along The Perimeter Reducing The Area Available For Planting By 40 Square Meters What Is The Width Of The Path 7546166 📰 Ft Ual Com Login Lines Stolenthis Is How Theyre Breaking Into Your Account 9851188 📰 Stop Waitingget Windows 10 Activation Fast With This Ultimate Guide 2766574 📰 Sania Maskatiya Shocking Revelation That Will Change Your Life Forever 2069667 📰 Best Airlines To Fly To Japan 3319223 📰 Detroit Pistons Vs Charlotte Hornets Match Player Stats 88785 📰 Stephen Fry And 2549907 📰 How Many Calories Does A Banana Have 8293159 📰 Football Games Video Games 3081713 📰 Hutch Dano 5091728 📰 Bright Purple 185141 📰 Interlachen Country Club 532479 📰 Treehouse Foods Stock Price 380050

Final Thoughts

Step 3: Apply the Distributive Property

The expression on the left is 4(4 + b) — you can think of (4 + b) as a parentheses that represents a single expression. To simplify, we use the distributive law:
a(b + c) = ab + ac

Here, a = 4, and the parentheses are (4 + b), so:
4(4 + b) = 4×4 + 4×b = 16 + 4b

Therefore, the original equation:
4 + b = 4² + 12
becomes:
4(4 + b) = 28

Step 4: Final Form and Verification

We now show the full simplification clearly:
Starting equation:
4 + b = 4² + 12
→
4(4 + b) = 28
since:

4² + 12 = 28
4(4 + b) = 16 + 4b

This simplified form makes it easier to solve for b by subtracting 4 from both sides:
b = 28 – 4 = 24

Hence, b = 24 — and verification confirms:
4 + 24 = 28, and
4² + 12 = 28, so the equation holds.