Question

(x+4)*(y-5)(5y^2+1)*(3y-3)(a-3)*(a^2+a-2)-3*(x+4)*(x-1)​

Answer 1

Ответ:

1. (х+4)×(у-5) = х(у-5)+4(у-5) = ху-5х+4у-20

объяснение: умножили вторую скобки на каждое слагаемое из первой скобки; распределили х и 4 через скобки.

2. (5у^2+1)×(3у-3) = 5у^2(3у-3)+1(3у-3) = 15у^3-15у^2+3у-3

объяснение: умножили вторую скобки на каждое слагаемое из первой скобки; распределили 5у^2 и 1 через скобки.

3. (а-3)×(а^2+а-2) = а(а^2+а-2)-3(а^2+а-2) = а^3+а^2-2а-3а^2-3а+6 = а^3-2а^2-5а+6

объяснение: умножили вторую скобки на каждое слагаемое из первой скобки; распределили а и -3 через скобки; привели подобные члены (а^2 и -3а^2), (-2а и -3а).

4. -3(х+4)(х-1) = (-3х-12)(х-1) = -3х^2+3х-12х+12 = -3х^2-9х+12

объяснение: распределили -3 через скобки; перемножили выражения в скобках; привели подобные члены (3х и -12х).

Answer 2

To simplify the given expression:

(x + 4)(y - 5)(5y^2 + 1)(3y - 3)(a - 3)(a^2 + a - 2) - 3(x + 4)(x - 1)

You can factor out common terms in both parts of the expression and then simplify:

1. Factor out (x + 4) from both terms: (x + 4)[(y - 5)(5y^2 + 1)(3y - 3)(a - 3)(a^2 + a - 2) - 3(x - 1)]

2. Now, let's simplify the part inside the brackets in the first term: (y - 5)(5y^2 + 1)(3y - 3)(a - 3)(a^2 + a - 2)

First, simplify the constants in the expression: (5y^2 + 1) and (a^2 + a - 2) are constants with respect to y, so you can simplify them: (5y^2 + 1)(a^2 + a - 2) = 5y^2a^2 + 5y^2a - 10y^2 + a^2 + a - 2

Now, simplify the rest of the expression: (y - 5)(3y - 3)(a - 3)

Expand this expression: (3y - 3)(y - 5)(a - 3) = 3(y - 1)(y - 5)(a - 3)

So, the first part becomes: (x + 4)[3(y - 1)(y - 5)(a - 3)(5y^2a^2 + 5y^2a - 10y^2 + a^2 + a - 2)]

3. Now, you can factor out the common factor 3(y - 1)(y - 5)(a - 3) from the expression inside the brackets: 3(y - 1)(y - 5)(a - 3)[(x + 4)(5y^2a^2 + 5y^2a - 10y^2 + a^2 + a - 2)]

4. The second term, -3(x - 1), can be simplified as follows: -3(x - 1) = -3x + 3

Now, the entire expression becomes: 3(y - 1)(y - 5)(a - 3)[(x + 4)(5y^2a^2 + 5y^2a - 10y^2 + a^2 + a - 2) - (x - 1)]

This is the simplified form of the given expression. If you need to expand it further, you can do so by multiplying out the remaining factors, but the expression is quite complex at this point.