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Question

Difficulty: EasyEvaluating Algebraic Expressions

If a=−4a = -4 and b=7b = 7, what is the value of the algebraic expression (a+b)2−3a(a + b)^2 - 3a?

  1. A
    -3
  2. B
    18
  3. 21Answer
  4. D
    45
  5. E
    77

Answer

21
Substituting a=−4a = -4 and b=7b = 7 into (a+b)2−3a(a + b)^2 - 3a gives ((−4)+7)2−3(−4)=(3)2+12=9+12=21((-4) + 7)^2 - 3(-4) = (3)^2 + 12 = 9 + 12 = 21.

Step-by-Step Solution

1
Substitute the given values into the expression
((−4)+7)2−3(−4)((-4) + 7)^2 - 3(-4)
Replace aa with −4-4 and bb with 77.
2
Simplify inside the parentheses
(3)2−3(−4)(3)^2 - 3(-4)
Following order of operations (PEMDAS), simplify −4+7=3-4 + 7 = 3 first.
3
Evaluate the exponent and multiplication
9+129 + 12
Square 33 to get 99, and multiply −3-3 by −4-4 to get +12+12.
4
Add the terms together
21
Combine 99 and 1212.

Key Concept

Evaluating Algebraic Expressions
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Topics

Evaluating Algebraic Expressions

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