1) [tex]A=6 a+\{a-2[a+3 b-4(a+b)]\}-13 a[/tex]
2) [tex]B=-[3 x-2 y+(x-2 y)-2(x+y)-3(2 x+1)]-(4 x+6 y)[/tex]
[tex]C=n-(x+y)-3(x-y)+2[-(x-2 y)-2(-x-y)]+2 x-10 y[/tex]
Answer (1)
To solve the mathematical expressions assigned to A, B, and C, let's simplify each expression step-by-step.
Expression for A:
A = 6 a + { a − 2 [ a + 3 b − 4 ( a + b )]} − 13 a
Let's simplify inside the brackets first:
a + 3 b − 4 ( a + b ) = a + 3 b − 4 a − 4 b
Simplify by combining like terms:
= − 3 a − b
Now substitute back into the expression:
A = 6 a + { a − 2 ( − 3 a − b )} − 13 a
Simplify inside the braces:
a + 6 a + 2 b
Simplifying further:
7 a + 2 b − 13 a
Combine the terms:
A = − 6 a + 2 b
Expression for B:
B = − [ 3 x − 2 y + ( x − 2 y ) − 2 ( x + y ) − 3 ( 2 x + 1 )] − ( 4 x + 6 y )
Simplifying inside each bracket:
3 x − 2 y + x − 2 y − 2 x − 2 y − 6 x − 3
Simplify further by combining like terms:
− 5 x − 6 y − 3
So:
B = − [ − 5 x − 6 y − 3 ] − 4 x − 6 y
Simplify further:
5 x + 6 y + 3 − 4 x − 6 y
Combine the terms:
B = x + 3
Expression for C:
C = n − ( x + y ) − 3 ( x − y ) + 2 [ − ( x − 2 y ) − 2 ( − x − y )] + 2 x − 10 y
Simplifying the part in square brackets first:
− ( x − 2 y ) − 2 ( − x − y ) = − x + 2 y + 2 x + 2 y = x + 4 y
Substituting back, we get:
C = n − x − y − 3 x + 3 y + 2 ( x + 4 y ) + 2 x − 10 y
Simplifying further:
= n − x − y − 3 x + 3 y + 2 x + 8 y + 2 x − 10 y
Combining the like terms results in:
C = n
With these simplifications, we have:
A = -6a + 2b
B = x + 3
C = n
The three expressions are simplified to these final results.
