Questions: Find the special product. (2x-7)^2

Transcript text: Find the special product. $(2 x-7)^{2}$

Solution

Solution Steps

To find the special product of $(2x - 7)^2$, we can use the formula for the square of a binomial: $(a - b)^2 = a^2 - 2ab + b^2$. Here, $a = 2x$ and $b = 7$. We will apply this formula to expand the expression.

Step 1: Identify the Binomial Terms

Given the expression $(2x - 7)^2$, we identify the terms:

$a = 2x$
$b = 7$

Step 2: Apply the Binomial Square Formula

We use the formula for the square of a binomial: \[ (a - b)^2 = a^2 - 2ab + b^2 \]

Step 3: Calculate Each Term

Substitute $a = 2x$ and $b = 7$ into the formula: \[ (2x)^2 = 4x^2 \] \[ 2 \cdot 2x \cdot 7 = 28x \] \[ 7^2 = 49 \]

Step 4: Combine the Terms

Combine the calculated terms to get the expanded form: \[ (2x - 7)^2 = 4x^2 - 28x + 49 \]

Final Answer

\[ \boxed{4x^2 - 28x + 49} \]

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