Question

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

Answer 1

Ответ:

a) 9

b) a⁴-b⁴

Объяснение:

a)  (x+1)²-(x-2)(x+4) = x²+2x+1 -(x²+4x-2x-8)= x²+2x+1 -(x²+2x-8) = x²+2x+1 -x²-2x+8 =9

б) (a+b)(a-b)(a²+b²)=(a²-b²)(a²+b²)= a⁴-b⁴

Answer 2

Sure, let's solve each expression 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) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8

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

Step 3: Distribute the negative sign: (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) = 0 + 0 + 9

Step 5: Simplify the expression: (x+1)^2 - (x-2)(x+4) = 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) = a^2 - ab + ab - b^2

Step 2: Simplify the expression: (a^2 - ab + ab - b^2) = a^2 - b^2

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

Step 3: Apply the difference of squares identity: (a^2 - b^2)(a^2 + b^2) = a^4 - b^4

So, the simplified expression is a^4 - b^4.

If you have any more expressions or questions, feel free to ask!