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Factor completely. 49v2−6449v^2-64

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Full solution

Q. Factor completely. 49v2−6449v^2-64
  1. Identify Expression Type: Step Title: Identify the Type of Expression\newlineConcise Step Description: Determine the type of algebraic expression and what method to use for factoring.\newlineStep Calculation: The expression 49v2−6449v^2 - 64 is a difference of squares because it is in the form a2−b2a^2 - b^2, where a=7va = 7v and b=8b = 8.
  2. Apply Squares Formula: Step Title: Apply the Difference of Squares Formula\newlineConcise Step Description: Use the difference of squares factoring formula, which is a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b).\newlineStep Calculation: Factoring 49v2−6449v^2 - 64 using the formula gives us (7v+8)(7v−8)(7v + 8)(7v - 8).
  3. Verify Factored Form: Step Title: Verify the Factored Form\newlineConcise Step Description: Check the factored form by multiplying the factors to see if it gives the original expression.\newlineStep Calculation: (7v+8)(7v−8)=49v2−56v+56v−64=49v2−64(7v + 8)(7v - 8) = 49v^2 - 56v + 56v - 64 = 49v^2 - 64, which matches the original expression.

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