Question

(а+7)^2+(а-7)(а+7)+12а-2x(1-x)+(2x-3)^2(5x-1)^2-25x^2=

Answer 1

(a+7)²+(a-7)(a+7)+12a-2x(1-x)+(2x-3)²*(5x-1)²-25x² = a2+14a+49+12a-2x+2x²+((2x-3)(5x-1))²-25x² = a²+14a+a²+12a-2x+2x²+(10x²-2x-15x+3)²-25x² = a²+14a+a²+12a-2x+2x²+(10x²-17x+3)²-25x² = a²+14a+a²+12a-2x+2x²+100x⁴+289x²+9-340x³+60x²-102x-25x² = 2a²+26a-104x+326x²+100x⁴+9-340x³

Answer 2

Let's simplify the given expression step by step:

1. Expand (а+7)^2: (а+7)^2 = (а+7)(а+7) = а^2 + 14а + 49

2. Expand (а-7)(а+7): (а-7)(а+7) = а^2 + 7а - 7а - 49 = а^2 - 49

3. Combine the above two expansions: (а+7)^2 + (а-7)(а+7) = (а^2 + 14а + 49) + (а^2 - 49) = 2а^2 + 14а

4. Now add the other terms: 2а^2 + 14а + 12а - 2x(1-x) + (2x-3)^2(5x-1)^2 - 25x^2

5. Expand (2x-3)^2: (2x-3)^2 = (2x-3)(2x-3) = 4x^2 - 12x + 9

6. Expand (5x-1)^2: (5x-1)^2 = (5x-1)(5x-1) = 25x^2 - 5x - 5x + 1 = 25x^2 - 10x + 1

7. Multiply the two expanded expressions from step 5 and 6: (2x-3)^2(5x-1)^2 = (4x^2 - 12x + 9)(25x^2 - 10x + 1) = 100x^4 - 140x^3 + 58x^2 - 18x + 9

Now the expression becomes: 2а^2 + 14а + 12а - 2x(1-x) + 100x^4 - 140x^3 + 58x^2 - 18x + 9 - 25x^2

8. Combine like terms: 2а^2 + 26а + 100x^4 - 140x^3 + 33x^2 - 18x + 9

So, the simplified expression is: 2а^2 + 26а + 100x^4 - 140x^3 + 33x^2 - 18x + 9