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2.1 Simplify the following expressions: 2.1.1 2a(3a + b) - 3a(2a + 4b). If a = -2, b = -4 and c = 6, find the value of these expressions: 2.1.2 abc/b. 2.1.3 Solve for x: 3^x = 81. 2.1.4 2^x − 1 = 15.

Mathematics

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Step-by-step solution

4 steps

To find the value of the expression abcb\frac{abc}{b} with the given values a=−2a = -2, b=−4b = -4, and c=6c = 6:

  1. Substitute the given values into the expression.

    abcb=(−2)(−4)(6)(−4)\frac{abc}{b} = \frac{(-2)(-4)(6)}{(-4)}

  2. Simplify the expression.

    You can cancel out the bb term from the numerator and the denominator, since b≠0b \neq 0.

    (−2)(−4)(6)(−4)=(−2)(6)\frac{(-2)(-4)(6)}{(-4)} = (-2)(6)

  3. Perform the multiplication.

    (−2)(6)=−12(-2)(6) = -12

    Alternatively, multiply the numerator first:

    (−2)(−4)(6)(−4)=(8)(6)−4=48−4\frac{(-2)(-4)(6)}{(-4)} = \frac{(8)(6)}{-4} = \frac{48}{-4}

  4. Perform the division.

    48−4=−12\frac{48}{-4} = -12

    The value of the expression is −12\boxed{-12}.

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