Expand the Expression: Finding (7b-3x)² Using Perfect Square Formula

Q: Why can't I just square each term separately?

Because (a - b)² ≠ a² - b²! When you multiply $ (7b - 3x)(7b - 3x) $, you get cross terms from the outer and inner products that create the middle term $ -42bx $.

Q: How do I remember the perfect square formula?

Think "First, Last, Twice the Middle": Square the first term, square the last term, then subtract (or add) twice the product of both terms. For $ (7b - 3x)^2 $: 49b² + 9x² - 2(7b)(3x).

Q: What if I have a plus sign instead of minus?

Use $ (a + b)^2 = a^2 + 2ab + b^2 $ instead! The only difference is the middle term becomes positive. The pattern stays the same: square both terms, then add twice their product.

Q: Do the variables need to be in alphabetical order?

No! Variables can be in any order. Whether you write $ 49b^2 - 42bx + 9x^2 $ or rearrange terms, the mathematical value stays identical.

Q: How can I check my answer without substituting values?

Count terms: Should have 3 terms for perfect squaresCheck signs: Pattern should be + - + for (a - b)² or + + + for (a + b)²Verify coefficients: Middle term coefficient = 2 × √(first coefficient) × √(last coefficient)

Perfect Square Formula with Multi-Variable Terms

Declares the given expression as a sum

$(7b-3x)^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 We'll use the shortened multiplication formulas to open the parentheses

00:27 When raising a product to a square, each factor is squared

00:39 Let's calculate the squares and products

00:50 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Declares the given expression as a sum

$(7b-3x)^2$

Step-by-step solution

To solve for $(7b - 3x)^2$ as a sum, we'll follow these steps:

Step 1: Identify the given expression and apply the formula for the square of a difference:
$(a - b)^2 = a^2 - 2ab + b^2$ where $a = 7b$ and $b = 3x$ .
Step 2: Expand each term:

$a^2 = (7b)^2 = 49b^2$
$-2ab = -2 \times 7b \times 3x = -42bx$
$b^2 = (3x)^2 = 9x^2$

Step 3: Combine all terms to form the sum:
$(7b - 3x)^2 = 49b^2 - 42bx + 9x^2$ .

Therefore, the solution to the problem is $(7b - 3x)^2 = 49b^2 - 42bx + 9x^2$ .

Hence, the correct answer choice is: $49b^2 - 42bx + 9x^2$

Final Answer

$49b^2-42bx+9x^2$

Key Points to Remember

Essential concepts to master this topic

Formula: (a - b)² = a² - 2ab + b² for all expressions
Technique: For (7b - 3x)²: (7b)² - 2(7b)(3x) + (3x)² = 49b² - 42bx + 9x²
Check: Verify middle term is -2 times product of first and last terms' roots ✓

Common Mistakes

Avoid these frequent errors

Forgetting the middle term in perfect square expansion
Don't just square the first and last terms like (7b - 3x)² = 49b² - 9x²! This misses the crucial middle term -2ab. The result lacks the cross-product term that comes from FOIL multiplication. Always include all three terms: a² - 2ab + b².

Practice Quiz

Test your knowledge with interactive questions

Declares the given expression as a sum

$$ (7b-3x)^2 $$

FAQ

Everything you need to know about this question

Why can't I just square each term separately?

Because (a - b)² ≠ a² - b²! When you multiply $(7b - 3x)(7b - 3x)$ , you get cross terms from the outer and inner products that create the middle term $-42bx$ .

How do I remember the perfect square formula?

Think "First, Last, Twice the Middle": Square the first term, square the last term, then subtract (or add) twice the product of both terms. For $(7b - 3x)^2$ : 49b² + 9x² - 2(7b)(3x).

What if I have a plus sign instead of minus?

Use $(a + b)^2 = a^2 + 2ab + b^2$ instead! The only difference is the middle term becomes positive. The pattern stays the same: square both terms, then add twice their product.

Do the variables need to be in alphabetical order?

No! Variables can be in any order. Whether you write $49b^2 - 42bx + 9x^2$ or rearrange terms, the mathematical value stays identical.

How can I check my answer without substituting values?

Count terms: Should have 3 terms for perfect squares
Check signs: Pattern should be + - + for (a - b)² or + + + for (a + b)²
Verify coefficients: Middle term coefficient = 2 × √(first coefficient) × √(last coefficient)

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Expand the Expression: Finding (7b-3x)² Using Perfect Square Formula

Perfect Square Formula with Multi-Variable Terms

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just square each term separately?

How do I remember the perfect square formula?

What if I have a plus sign instead of minus?

Do the variables need to be in alphabetical order?

How can I check my answer without substituting values?

🌟 Unlock Your Math Potential

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