Answer:
[tex]3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b[/tex]
[tex]y (10 - y) + 3 (y - 2) = - y^2+13y - 6[/tex]
[tex]2 (8a - 5b) + 3 (5a - 12) = 31a -10b - 36[/tex]
[tex]3 (y - 3) + ( 8 - 6y + x) = -3y + x-1[/tex]
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + b^2 - bc[/tex]
[tex]5 (x - y + z) + (4x + 3y) =9x - 2y +5z[/tex]
Step-by-step explanation:
Solving (i):
[tex]3 (a + 5b) + a (a + 4)[/tex]
Open brackets
[tex]3 (a + 5b) + a (a + 4) = 3a + 15b + a^2 + 4a[/tex]
Collect like terms
[tex]3 (a + 5b) + a (a + 4) = a^2 + 4a+3a + 15b[/tex]
[tex]3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b[/tex]
Solving (ii)
[tex]y (10 - y) + 3 (y - 2)[/tex]
Open bracket
[tex]y (10 - y) + 3 (y - 2) = 10y - y^2 + 3y - 6[/tex]
Collect like terms
[tex]y (10 - y) + 3 (y - 2) = - y^2+10y + 3y - 6[/tex]
[tex]y (10 - y) + 3 (y - 2) = - y^2+13y - 6[/tex]
Solving (iii)
[tex]2 (8a - 5b) + 3 (5a - 12)[/tex]
Open bracket
[tex]2 (8a - 5b) + 3 (5a - 12) = 16a -10b + 15a - 36[/tex]
Collect like terms
[tex]2 (8a - 5b) + 3 (5a - 12) = 16a+ 15a -10b - 36[/tex]
[tex]2 (8a - 5b) + 3 (5a - 12) = 31a -10b - 36[/tex]
Solving (iv)
[tex]3 (y - 3) + ( 8 - 6y + x)[/tex]
Open bracket
[tex]3 (y - 3) + ( 8 - 6y + x) = 3y - 9 + 8 - 6y + x[/tex]
Collect like terms
[tex]3 (y - 3) + ( 8 - 6y + x) = 3y - 6y + x- 9 + 8[/tex]
[tex]3 (y - 3) + ( 8 - 6y + x) = -3y + x-1[/tex]
Solving (v):
[tex]a (a - 2b) + b (b + 2a - c)[/tex]
Open bracket
[tex]a (a - 2b) + b (b + 2a - c) =a^2 - 2ab + b^2 + 2ab - bc[/tex]
Collect like terms
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + 2ab- 2ab + b^2 - bc[/tex]
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + b^2 - bc[/tex]
Solving (vi)
[tex]5 (x - y + z) + (4x + 3y)[/tex]
Open brackets
[tex]5 (x - y + z) + (4x + 3y) =5x - 5y +5z+4x +3y[/tex]
Collect like terms
[tex]5 (x - y + z) + (4x + 3y) =5x +4x +3y- 5y +5z[/tex]
[tex]5 (x - y + z) + (4x + 3y) =9x - 2y +5z[/tex]
