Evaluate the algebraic expression P = 4v^3 - 3uv + 2u^2 using the assigned values u = -4 a… — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the algebraic expression $P = 4v^3 - 3uv + 2u^2$ using the assigned values $u = -4$ and $v = -2$ . Fill in the missing numerical values for the intermediate calculation step and the final evaluated result.

Cevap:The calculated value for the isolated term

4v^3

is 【-32】, which makes the final evaluated total for the entire expression

P

equal to 【-24】.

Cevap

The first term evaluates to -32, and the entire expression evaluates to -24.

The expression requires careful substitution of

u = -4

and

v = -2

. Following the order of operations (PEMDAS), we first calculate the exponents:

(-2)^3 = -8

and

(-4)^2 = 16

. Next, we perform the multiplication for each term:

4(-8) = -32

-3(-4)(-2) = -24

, and

2(16) = 32

. Finally, combining these intermediate values gives

-32 - 24 + 32 = -24

Adım Adım Çözüm

Substitute the value of v into the first term

4v^3

and evaluate according to the order of operations.

4(-2)^3 = 4(-8) = -32

Exponents must be evaluated before multiplication. The cube of a negative number remains negative.

Substitute the values of u and v into the second term

-3uv

and evaluate.

-3(-4)(-2) = -3(8) = -24

Multiplying two negative numbers yields a positive product, which is then multiplied by the negative coefficient.

Substitute the value of u into the third term

2u^2

and evaluate.

2(-4)^2 = 2(16) = 32

The square of a negative number is positive. This must be calculated before multiplying by the coefficient.

Combine the evaluated terms to find the final total for P.

-32 - 24 + 32 = -24

Adding and subtracting the values from left to right yields the final result.

Anahtar Kavram

Evaluating multi-variable algebraic expressions by correctly substituting negative integers and rigorously applying the order of operations.

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