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Zorluk: KolayEvaluating Algebraic Expressions

If a=−4a = -4 and b=3b = 3, what is the value of the expression 3a2−2ab3a^2 - 2ab?

  1. 72Cevap
  2. B
    24
  3. C
    -24
  4. D
    168
  5. E
    0

Cevap

72
Substituting a=−4a = -4 and b=3b = 3 yields 3(−4)2−2(−4)(3)=3(16)−(−24)=48+24=723(-4)^2 - 2(-4)(3) = 3(16) - (-24) = 48 + 24 = 72.

Adım Adım Çözüm

1
Substitute the given values into the expression
Replace aa with −4-4 and bb with 33 in 3a2−2ab3a^2 - 2ab to get 3(−4)2−2(−4)(3)3(-4)^2 - 2(-4)(3).
Direct substitution of known variable values.
2
Evaluate the exponent
(−4)2=16(-4)^2 = 16, so the term 3(−4)23(-4)^2 becomes 3(16)=483(16) = 48.
Exponents must be evaluated before multiplication according to PEMDAS.
3
Evaluate the second multiplication term
2ab=2(−4)(3)=−242ab = 2(-4)(3) = -24.
Multiply the numerical factors together.
4
Subtract the terms to find the final value
48−(−24)=48+24=7248 - (-24) = 48 + 24 = 72.
Subtracting a negative number is equivalent to adding its positive value.

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Evaluating Algebraic Expressions with Negative Values
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Evaluating Algebraic Expressions

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