289/900 is the simplified form of the expression ( -1/3 + 0.3( -1/3 ) + 1 )².
What is the simplified form of the given expression?
Given the expression in the question;
( -1/3 + 0.3( -1/3 ) + 1 )²
To simplify, first convert 0.3 from to decimal to fraction.
Replace 0.3 with 3/10
( -1/3 + (3/10)( -1/3 ) + 1 )²
Multiply (3/10) and ( -1/3 )
( -1/3 - (3×1 / 10×3 ) + 1 )²
( -1/3 - (3 / 30 ) + 1 )²
Cancel out the common factor (3)
( -1/3 - 1/10 + 1 )²
Next find the common denominator
( -1/3×10/10 - 1/10×3/3 + 1×30/30 )²
( -10/30 - 3/30 + 30/30 )²
Combine the numerators over common denominators
( ( -10 - 3 + 30 ) / 30 )²
( ( -13 + 30 ) / 30 )²
( 17 / 30 )²
Apply product rule
17² / 30²
289/900
Therefore, the simplified form of the expression is 289/900.
Learn more about algebraic expressions here: brainly.com/question/4344214
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