John Frank
09/06/2023 · Senior High School
Multiply using the rule for the product of the sum and difference of two terms. \[ (4 x+5)(4 x-5) \] \( (4 x+5)(4 x-5)=\square \)
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To multiply the expression \((4x + 5)(4x - 5)\), we can use the rule for the product of the sum and difference of two terms, which is also known as the difference of squares. The formula is:
\[ (a + b)(a - b) = a^2 - b^2 \]
In this case, \(a = 4x\) and \(b = 5\). Plugging these values into the formula, we get:
\[ (4x + 5)(4x - 5) = (4x)^2 - 5^2 \]
Now, we calculate the squares:
\[ (4x)^2 = 16x^2 \]
\[ 5^2 = 25 \]
Substitute these back into the formula:
\[ 16x^2 - 25 \]
So, the product of \((4x + 5)(4x - 5)\) is:
\[ 16x^2 - 25 \]
Quick Answer
\[ 16x^2 - 25 \]
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