Answer:
The complete table is:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]
+ + + +
[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ 7a + 2b ] + [ 3a + 8 ] + [ 0 ] = [10a + 2b + 8 ]
Explanation:
You can determine the content of each box by subtraction, running the rows and the columns.
The expressions are:
[ 5a ] + [ ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ ] = [ ]
+ + + +
[ ] + [ ] + [ -3a ] = [ 1 ]
= = = =
[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
1. First row:
[ 5a ] + [ ] + [ 4a ] = [ 10a + 3 ]
[ ] = [10a+ 3] - [ 4a ] - [ 5a ] = 10a - 4a - 5a + 3 = a + 3
2. Second colum:
[ a + 3 ] + [ 4 + a ] + [ ] = [ 3a + 8 ]
[ ] = [ 3a + 8 ] - [ a + 3 ] - [ 4 + a ] = 3a - a + a + 8 - 4 - 3 = a + 1
So far, you have completed this:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ ] = [ ]
+ + + +
[ ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
3. Complete the row 3:
[ ] + [ a + 1 ] + [ -3a ] = [ 1 ]
[ ] = [ 1 ] - [ a + 1 ] - [ -3a ] = - a + 3a + 1 - 1 = 2a
So far, you have completed this:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ ] = [ ]
+ + + +
[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
4. Complete the fourth column:
[ 10a + 3 ] + [ ] + [ 1 ] = [10a + 2b + 8 ]
[ ] = 10a + 2b + 8 - 10a - 3 - 1 = 2b + 4
So far, this is the results:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ ] = [ 2b + 4 ]
+ + + +
[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
5. Complete the second row:
[ 2b ] + [ 4 + a ] + [ ] = [ 2b + 4 ]
[ ] = [ 2b + 4 ] - [ 2b ] - [ 4 + a ] = 2b - 2b + 4 - 4 - a = - a
So far:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]
+ + + +
[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
6. Complete the first colum:
[ 5a ] + [ 2b ] + [2a ] = [ ]
[ ] = [ 7a + 2b ]
So far:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]
+ + + +
[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ 7a + 2b ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
7. Complete the last row:
[ 7a + 2b ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]
[ ] = [10a + 2b + 8 ] - [ 7a + 2b ] - [ 3a + 8 ] = 0
The complete table is:
[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]
+ + + +
[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]
+ + + +
[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]
= = = =
[ 7a + 2b ] + [ 3a + 8 ] + [ 0 ] = [10a + 2b + 8 ]
