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If x = -7 and y = 3, calculate the value of: (x + y) x2 + y2 27x2 - 12y2

Mathematics

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Answers

4 parts
a

425\frac{4}{25}

b
35
c
1215
d

127\frac{12}{7}

Step-by-step solution

14 steps

Here are the calculations for each part:

Given x=−7x = -7 and y=3y = 3.

Part a· 3 steps

Calculate (x+y)2(x−y)2\frac{(x+y)^2}{(x-y)^2}.

  1. Substitute the values of xx and yy into the expression.

    (−7+3)2(−7−3)2\frac{(-7+3)^2}{(-7-3)^2}

  2. Simplify the numerator and the denominator.

    (−4)2(−10)2=16100\frac{(-4)^2}{(-10)^2} = \frac{16}{100}

  3. Simplify the fraction.

    16100=425\frac{16}{100} = \frac{4}{25}

    The value is 425\boxed{\frac{4}{25}}.

Part b35

Calculate 2x2+xy22x^2 + xy^2.

  1. Substitute the values of xx and yy into the expression.

    2(−7)2+(−7)(3)22(-7)^2 + (-7)(3)^2

  2. Evaluate the powers.

    2(49)+(−7)(9)2(49) + (-7)(9)

  3. Perform the multiplications.

    98−6398 - 63

  4. Perform the subtraction.

    3535

    The value is 35\boxed{35}.

Part c1215

Calculate 27x2−12y227x^2 - 12y^2.

  1. Substitute the values of xx and yy into the expression.

    27(−7)2−12(3)227(-7)^2 - 12(3)^2

  2. Evaluate the powers.

    27(49)−12(9)27(49) - 12(9)

  3. Perform the multiplications.

    1323−1081323 - 108

  4. Perform the subtraction.

    12151215

    The value is 1215\boxed{1215}.

Part d

127\frac{12}{7}

Calculate 3x+y2x\frac{3x+y^2}{x}.

  1. Substitute the values of xx and yy into the expression.

    3(−7)+(3)2−7\frac{3(-7)+(3)^2}{-7}

  2. Simplify the numerator.

    −21+9−7=−12−7\frac{-21+9}{-7} = \frac{-12}{-7}

  3. Simplify the fraction.

    −12−7=127\frac{-12}{-7} = \frac{12}{7}

    The value is 127\boxed{\frac{12}{7}}.

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