Pregunta
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The product of \( (x-7)^2 \) is \( x^2 - 14x + 49 \).
Solución
1. Write the expression as a product of two binomials:
\[
(x-7)^2 = (x-7)(x-7)
\]
2. Multiply the two binomials using the distributive property (FOIL method):
\[
(x-7)(x-7) = x \cdot x + x \cdot (-7) -7 \cdot x -7 \cdot (-7)
\]
3. Perform the multiplications:
\[
x \cdot x = x^2,\quad x \cdot (-7) = -7x,\quad -7 \cdot x = -7x,\quad -7 \cdot (-7) = 49
\]
4. Combine like terms:
\[
x^2 - 7x - 7x + 49 = x^2 - 14x + 49
\]
The final expanded product is:
\[
x^2 - 14x + 49
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Extra Insights
To find the product of \( (x-7)^{2} \), we can use the formula for squaring a binomial, which states \( (a-b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = x \) and \( b = 7 \). So, applying the formula: \[ (x-7)^{2} = x^{2} - 2(x)(7) + 7^{2} \] This simplifies to: \[ x^{2} - 14x + 49 \] Thus, the product is: \[ x^{2} - 14x + 49 \]
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