Question

4(a-1)^2 +(a-2)(6-a)-135(a-4)^2 - (a-4)(7-a)-18a+6

Answer 1

4(a²-2a+1)+6a-a²-12+2a-13= 4a²-8a+4+6a-a²-12+2a-13= 3a²-21

5(a²-8a+16)-7a+a²+28-4a-18a+6= 5a²-40a+80-7a+a²+28-4a-18a+6= 6a²-69a+114

Answer 2

To simplify the given expression, let's expand and combine like terms:

1. Expand the squared terms: (a - 1)^2 = (a - 1)(a - 1) = a^2 - 2a + 1, (a - 4)^2 = (a - 4)(a - 4) = a^2 - 8a + 16.

2. Expand the other terms: (a - 2)(6 - a) = 6a - 2a - 6 + 2 = 4a - 4, (a - 4)(7 - a) = 7a - 4a - 28 + 4 = 3a - 24.

Now the expression becomes:

4(a - 1)^2 + (a - 2)(6 - a) - 135(a - 4)^2 - (a - 4)(7 - a) - 18a + 6

Replace the squared terms and the expanded terms:

= 4(a^2 - 2a + 1) + (4a - 4) - 135(a^2 - 8a + 16) - (3a - 24) - 18a + 6

Now distribute the constants:

= 4a^2 - 8a + 4 + 4a - 4 - 135a^2 + 1080a - 2160 - 3a + 24 - 18a + 6

Combine like terms:

= (4a^2 - 135a^2) + (-8a + 4a - 3a - 18a) + (4 - 4 + 24 + 6) + (-2160 + 1080)

= -131a^2 - 25a - 2130

So, the simplified expression is -131a^2 - 25a - 2130.