Question

Evaluate the expression. 1/2 - 4 (1/2 + 1)^2

A.-9

B. 9/4

C. 17/2

D. -17/2

Answer 1

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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`(1)/(2)-4\left((1)/(2)+1\right)^2=(1)/(2)-4\left(1(1)/(2)\right)^2=(1)/(2)-4\left((1\cdot2+1)/(2)\right)^2\\\\=(1)/(2)-4\left((3)/(2)\right)^2=(1)/(2)-4\cdot(3^2)/(2^2)=(1)/(2)-4\cdot(9)/(4)=(1)/(2)-1\cdot(9)/(1)\\\\=(1)/(2)-9=\boxed{-8(1)/(2)=-(8\cdot2+1)/(2)=\boxed{-(17)/(2)}}\to\boxed{D.}`

Answer 2

D. -17/2

Explanation:

1/2 - 4 (1/2 + 1)^2

First we evaluate what is inside the parentheses

1/2 - 4 (3/2) ^2

Now we square what is inside the parentheses

1/2 - 4(9/4)

Now multiply

1/2 -9

Get a common denominator 9 = 9 *2/2 = 18/2

1/2 - 18/2

-17/2