What is factor abc+ab+ac+bc+a+b+c+1 ?

The solution to factor abc+ab+ac+bc+a+b+c+1 is (1+a)(c+1)(b+1)

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factor abc+ab+ac+bc+a+b+c+1

factor

ab c + ab + a c + b c + a + b + c + 1

(1 + a) (c + 1) (b + 1)

Solution steps

ab c + ab + a c + b c + a + b + c + 1

Factor out common term

ba

= ba (c + 1) + a c + b c + a + b + c + 1

Factor out common term

b

= b (a (1 + c) + c + 1) + a c + a + 1 + c

Factor

a (c + 1) + c + 1 : (c + 1) (a + 1)

= a c + a + b (c + 1) (a + 1) + c + 1

Rewrite as

= (1 + a) b (1 + c) + a c + c + 1 \cdot (1 + a)

Factor out common term

(1 + a)

= (1 + a) (b (1 + c) + 1) + a c + c

Factor out common term

c

= (1 + a) (1 + (1 + c) b) + c (a + 1)

Factor out common term

(1 + a)

= (1 + a) (1 + (1 + c) b + c)

Factor

b (c + 1) + c + 1 : (c + 1) (b + 1)

= (a + 1) (c + 1) (b + 1)

\frac{( x + 2 ) ^{2} - 4}{x}

sin (2 x + 10)

x^{2 - 4 x + 10}

- (3.4)

a x + b x + c x + a y + b y + cy - a - b - c

What is factor abc+ab+ac+bc+a+b+c+1 ?
The solution to factor abc+ab+ac+bc+a+b+c+1 is (1+a)(c+1)(b+1)