Question

(2а+3)(а-3)-2а(4-а) (1-х)(х-1)+(х-1) (а+в)(а-2в)+(2в-а)(2в+а)

Answer 1

1)(2a+3)(a-3)-2a(4-a)=2a²-6a+3a-9-8a+2a²=4a²-11a-9
2)(1-x)(x-1)+(x-1)=x-1-x²-x=1-x²+x-1=-x²-x
3)(a+b)(a-2b)+(2b-a)(2b+a)=a²-2ab+ab-2b²+4b²-a²=-ab-2b²

Answer 2

Let's simplify the given expressions step by step:

1. (2а+3)(а-3) - 2а(4-а) Expand the first bracket: (2а+3)(а-3) = 2а(а) + 2а(-3) + 3(а) + 3(-3) = 2а^2 - 6а + 3а - 9

Now, the second part:

• 2а(4-а) = -2а(4) + 2а(а) = -8а + 2а^2

Now, combine both parts: (2а+3)(а-3) - 2а(4-а) = 2а^2 - 6а + 3а - 9 - 8а + 2а^2

Combine like terms: = 4а^2 - 11а - 9

2. (1-х)(х-1) + (х-1) Expand the first bracket: (1-х)(х-1) = 1(х) + 1(-1) - х(х) - х(-1) = х - 1 - х^2 + х

Now, add (х-1) to the above result: = х - 1 - х^2 + х + х - 1

Combine like terms: = -х^2 + 2х - 2

3. (а+в)(а-2в) + (2в-а)(2в+а) Expand the first bracket: (а+в)(а-2в) = а(а) + а(-2в) + в(а) + в(-2в) = а^2 - 2ва + ва - 2в^2

Now, expand the second bracket: (2в-а)(2в+а) = 2в(2в) + 2в(а) - а(2в) - а(а) = 4в^2 + 2ва - 2ва - а^2

Combine both parts: (а+в)(а-2в) + (2в-а)(2в+а) = а^2 - 2ва + ва - 2в^2 + 4в^2 + 2ва - 2ва - а^2

Combine like terms: = а^2 + 2в^2

So the simplified expressions are:

1. 4а^2 - 11а - 9
2. -х^2 + 2х - 2
3. а^2 + 2в^2