Question

Difficulty: EasyEvaluating Algebraic Expressions

Evaluate the algebraic expression for the given variable values.

Answer:When p=3p = -3 and q=4q = 4, the value of the expression 2p25q+12p^2 - 5q + 1 is 【-1】.

Answer

The value of the expression is -1.
Substituting p=3p = -3 and q=4q = 4 into 2p25q+12p^2 - 5q + 1 yields 2(3)25(4)+1=2(9)20+1=1820+1=12(-3)^2 - 5(4) + 1 = 2(9) - 20 + 1 = 18 - 20 + 1 = -1.

Step-by-Step Solution

1
Substitute the given values p=3p = -3 and q=4q = 4 into the expression 2p25q+12p^2 - 5q + 1.
2(3)25(4)+12(-3)^2 - 5(4) + 1
Replace each variable with its assigned value.
2
Evaluate the exponent (3)2(-3)^2.
2(9)5(4)+12(9) - 5(4) + 1
Exponents must be evaluated before multiplication according to the order of operations.
3
Perform the multiplication operations.
18 - 20 + 1
2×9=182 \times 9 = 18 and 5×4=205 \times 4 = 20.
4
Add and subtract from left to right.
-1
1820=218 - 20 = -2, and 2+1=1-2 + 1 = -1.

Key Concept

Evaluating Algebraic Expressions
Estimated Time:45s
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