Question

А) (x+1)^2-(x-2)(x+4) б) (a+b) (a-b) (a^2+b^2) С решением

Answer 1

Ответ: a) 9 б) a^4 - b^4

Объяснение:

а) (х+1)^2 - (x-2)(x+4) = x^2 + 2x + 1 - x^2 - 4x +2x + 8 = 9

б) (a+b)(a-b)(a^2+b^2) = (a^2 - ab + ab - b^2)(a^2+b^2) = (a^2 - b^2)(a^2 + b^2) = a^4 + a^2b^2 - a^2b^2 - b^4 = a^4 - b^4

Answer 2

Let's simplify the given expressions step by step:

a) (x+1)^2 - (x-2)(x+4)

Step 1: Expand (x+1)^2 (x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1

Step 2: Expand (x-2)(x+4) (x-2)(x+4) = xx + x4 - 2x - 24 = x^2 + 4x - 2x - 8 = x^2 + 2x - 8

Now, the expression becomes: (x+1)^2 - (x-2)(x+4) = (x^2 + 2x + 1) - (x^2 + 2x - 8)

Step 3: Distribute the negative sign to the terms inside the parentheses: (x^2 + 2x + 1) - (x^2 + 2x - 8) = x^2 + 2x + 1 - x^2 - 2x + 8

Step 4: Combine like terms: (x^2 - x^2) + (2x - 2x) + (1 + 8) = 0x + 0 + 9

Step 5: Simplify: 0x + 0 + 9 = 9

So, the simplified expression is 9.

b) (a+b)(a-b)(a^2+b^2)

Step 1: Expand (a+b)(a-b) (a+b)(a-b) = aa - ab + ba - bb = a^2 - ab + ba - b^2

Step 2: Simplify the middle term (ab - ba): Since ab and ba are like terms, they cancel out: a^2 - ab + ba - b^2 = a^2 - b^2

Step 3: Now, the expression becomes: (a+b)(a-b)(a^2+b^2) = (a^2 - b^2)(a^2 + b^2)

Step 4: Use the difference of squares formula (a^2 - b^2 = (a+b)(a-b)): (a^2 - b^2)(a^2 + b^2) = (a+b)(a-b)(a^2 + b^2)

So, the simplified expression is (a+b)(a-b)(a^2+b^2).

Note: It's essential to be careful with sign changes while expanding and simplifying expressions. Also, make sure to recognize common algebraic identities like the difference of squares formula.