Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

The expression (𝑎^6−𝑏^6)equals... [A] (𝑎^3−𝑏^3)^2 [B] (𝑎^2−𝑏^2)^3 [C] (𝑎−𝑏)^6 [D] none of these?

math.  please show workings please

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  • 1 month ago

    The only working necessary is that (X + Y)^n has n+1 terms in the expansion.  None of those will be "like terms" that can be combined unless Y is a constant multiple of X.

    Since a^6 - b^6 has only two terms, but choices [A] through [C] all have 3 or more terms, then none of them can be equivalent.

  • 1 month ago

    A = (a³ - b³)²

    A = (a³)² - 2a³b³ + (b³)²

    A = a⁶ - 2a³b³ + b⁶

    A ≠ a⁶ - b⁶

    B = (a² - b²)³

    B = (a² - b²)².(a² - b)

    B = (a⁴ - 2a²b² + b⁴).(a² - b)

    B = a⁶ - a⁴b - 2a⁴b² + 2a²b³ + a²b⁴ - b⁵

    B ≠ a⁶ - b⁶

    C = (a - b)⁶

    C = [(a - b)²]³

    C = [a² - 2ab + b²]³

    C = [a² - 2ab + b²]².[a² - 2ab + b²]

    C = [a⁴ - 2a³b + a²b² - 2a³b + 4a²b² - 2ab³ + a²b² - 2ab³ + b⁴].[a² - 2ab + b²]

    C = [a⁴ + 6a²b² - 4a³b - 4ab³ + b⁴].[a² - 2ab + b²]

    C = a⁶ - 2a⁵b + a⁴b² + 6a⁴b² - 12a³b³ + 6a²b⁴ - 4a⁵b + 8a⁴b² - 4a³b³ - 4a³b³ + 8a²b⁴ - 4ab⁵ + a²b⁴ - 2ab⁵ + b⁶

    C = a⁶ - 6a⁵b + 15a⁴b² - 20a³b³ + 15a²b⁴ - 6ab⁵ + b⁶

    C ≠ a⁶ - b⁶

    …to you to conclude

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