Question

(a+b+c) (ab + b + ac) - abc​

Answer 1

Ответ:

(a+b)(a+c)(b+c)

Пошаговое объяснение:

(a+b+c)(ab+ac+bc)-abc=а²b+a²c+ab²+2abc+ac²+b²c+bc²=(a+b)c² + (a²+2ab+b²)c+(a²b+ab²)=(a+b)(c²+(a+b)c+ab)=(a+b)(c²+(ac+bc)+ab)=(a+b)(c²+ac+bc+ab)=(a+b)(ab+ac+bc+c²)=(a+b)((a+c)b+(ac+c²))=(a+b)((a+c)1b+(a+c)c)=(a+b)((a+c)(1b+c))=(a+b)((a+c)(b+c))=(a+b)(a=c)(b+c).

Answer 2

To simplify the expression (a+b+c)(ab+b+ac) - abc, you can use the distributive property to expand it and then simplify further. Here are the steps:

1. Distribute the terms inside the first parentheses: (a+b+c)(ab+b+ac) = a(ab+b+ac) + b(ab+b+ac) + c(ab+b+ac)

2. Now, distribute the terms inside each of these three terms: a(ab+b+ac) = a^2b + ab^2 + a^2c b(ab+b+ac) = ab^2 + b^2 + abc c(ab+b+ac) = ac^2 + b^2c + abc

3. Now, combine these terms: a^2b + ab^2 + a^2c + ab^2 + b^2 + abc + ac^2 + b^2c + abc

4. Simplify further by combining like terms: a^2b + 2ab^2 + a^2c + b^2 + 2abc + ac^2 + b^2c

5. Finally, subtract abc: a^2b + 2ab^2 + a^2c + b^2 + 2abc + ac^2 + b^2c - abc

This is the simplified form of the expression (a+b+c)(ab+b+ac) - abc.