Test each algebra statement to see whether they appear to be true in general. If a statement appears always to be true, draw a diagram to justify the statement. Add an explanation if the diagram is not self-explanatory. If a statement is not true in general, give a counterexample.
A) $\frac { a } { b + c } = \frac { a } { b } + \frac { a } { c }$
B) $( a + b ) - ( c + d ) = ( a - c ) + ( b - d )$
C) $( a + b ) ^ { 2 } = a ^ { 2 } + b ^ { 2 }$
D) $( a + b ) ^ { 3 } = a ^ { 3 } + b ^ { 3 }$
E) $( a - b ) + c = a - ( b + c )$

Question

Test each algebra statement to see whether they appear to be true in general. If a statement appears always to be true, draw a diagram to justify the statement. Add an explanation if the diagram is not self-explanatory. If a statement is not true in general, give a counterexample.
A) $\frac { a } { b + c } = \frac { a } { b } + \frac { a } { c }$ 
B) $( a + b ) - ( c + d ) = ( a - c ) + ( b - d )$ 
C) $( a + b ) ^ { 2 } = a ^ { 2 } + b ^ { 2 }$ 
D) $( a + b ) ^ { 3 } = a ^ { 3 } + b ^ { 3 }$ 
E) $( a - b ) + c = a - ( b + c )$

Quizplus · Accepted Answer

The Answer is A) Not true in general; student should have shown a counterexample.
B) True. Sample diagram:

A) Not true in general; student should have shown a counterexample. B) True. Sample diagram: C) Not true in general; student should have shown a counterexample. D) Not true in general; student should have shown a counterexample. E) Not true in general; student should have shown a counterexample.

C) Not true in general; student should have shown a counterexample.
D) Not true in general; student should have shown a counterexample.
E) Not true in general; student should have shown a counterexample.

Test Each Algebra Statement to See Whether They Appear to Be