Question

properties of exponents and order of operations
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expand the following expression, and combine any like terms:
$(x + 7)^2 - (x - 3)^2$
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Explanation:

Step1: Expand the squares using \((a+b)^2 = a^2 + 2ab + b^2\) and \((a - b)^2 = a^2 - 2ab + b^2\)

\((x + 7)^2 = x^2 + 14x + 49\)
\((x - 3)^2 = x^2 - 6x + 9\)

Step2: Substitute the expanded forms into the original expression

\((x^2 + 14x + 49) - (x^2 - 6x + 9)\)

Step3: Distribute the negative sign

\(x^2 + 14x + 49 - x^2 + 6x - 9\)

Step4: Combine like terms

\((x^2 - x^2) + (14x + 6x) + (49 - 9) = 20x + 40\)

Answer:

\(20x + 40\)