we want to factor the following expression: (x - 3)^2 - 64y^4. we can factor the expression as (u + v)(u…

we want to factor the following expression: (x - 3)^2 - 64y^4. we can factor the expression as (u + v)(u - v) where u and v are either constant integers or single - variable expressions. 1) what are u and v? choose 1 answer: a u=(x - 3) and v = 8y b u=(x - 3) and v = 8y^2 c u=(x - 3) and v = 64y^4 d u=(x - 3)^2 and v = 8y e u=(x - 3)^2 and v = 8y^2 f u=(x - 3)^2 and v = 64y^4 2) factor the expression.

we want to factor the following expression: (x - 3)^2 - 64y^4. we can factor the expression as (u + v)(u - v) where u and v are either constant integers or single - variable expressions. 1) what are u and v? choose 1 answer: a u=(x - 3) and v = 8y b u=(x - 3) and v = 8y^2 c u=(x - 3) and v = 64y^4 d u=(x - 3)^2 and v = 8y e u=(x - 3)^2 and v = 8y^2 f u=(x - 3)^2 and v = 64y^4 2) factor the expression.

Answer

Explanation:

Step1: Recall difference - of - squares formula

The difference - of - squares formula is (a^{2}-b^{2}=(a + b)(a - b)). In the given expression ((x - 3)^{2}-64y^{4}), we can rewrite (64y^{4}=(8y^{2})^{2}), where (a=(x - 3)) and (b = 8y^{2}).

Step2: Identify (U) and (V)

Comparing ((x - 3)^{2}-64y^{4}) with ((U + V)(U - V)), we have (U=(x - 3)) and (V = 8y^{2}).

Step3: Factor the expression

Using the difference - of - squares formula ((a^{2}-b^{2})=(a + b)(a - b)) with (a=(x - 3)) and (b = 8y^{2}), we get ((x - 3)^{2}-64y^{4}=((x - 3)+8y^{2})((x - 3)-8y^{2})=(x - 3+8y^{2})(x - 3 - 8y^{2})).

Answer:

  1. B. (U=(x - 3)) and (V = 8y^{2})
  2. ((x - 3+8y^{2})(x - 3 - 8y^{2}))