Examkin

Soru

Zorluk: OrtaEvaluating Algebraic Expressions

Evaluate the algebraic expression 3a2b−4bca−c\frac{3a^2b - 4bc}{a - c} given that a=−2a = -2, b=3b = 3, and c=−5c = -5. What is the final numerical value?

Cevap: 32

Cevap

The numerical value of the expression is 32.
After properly substituting the given values, evaluating the exponents, and following the order of operations, the numerator calculates to 96 and the denominator simplifies to 3. The final division of 96 by 3 yields 32.

Adım Adım Çözüm

1
Substitute the assigned values of aa, bb, and cc into the given algebraic expression.
3(−2)2(3)−4(3)(−5)−2−(−5)\frac{3(-2)^2(3) - 4(3)(-5)}{-2 - (-5)}
Direct variable substitution is required to compute the numerical value.
2
Evaluate the exponent applied to the negative base.
(−2)2=4(-2)^2 = 4
According to the order of operations (PEMDAS), exponents must be resolved prior to multiplication.
3
Carry out the multiplication operations in the numerator.
3(4)(3)=363(4)(3) = 36 and 4(3)(−5)=−604(3)(-5) = -60
Multiplication is processed from left to right within the grouping of the numerator.
4
Complete the subtraction operation in the numerator.
36−(−60)=36+60=9636 - (-60) = 36 + 60 = 96
Subtracting a negative quantity is algebraically identical to adding its positive counterpart.
5
Evaluate the subtraction operation in the denominator.
−2−(−5)=−2+5=3-2 - (-5) = -2 + 5 = 3
The entire denominator acts as a single grouping and must be fully simplified before division.
6
Divide the evaluated numerator by the evaluated denominator.
963=32\frac{96}{3} = 32
This final arithmetic step produces the precise evaluation of the fractional expression.

Anahtar Kavram

Evaluating complex rational algebraic expressions using substitution and the order of operations with signed integers.
Bu soruyu puanla

Konular

Evaluating Algebraic Expressions

Bu konudan daha fazla soru