What is factor x^yy^x+xy+x^{y+1}+y^{x+1} ?

The solution to factor x^yy^x+xy+x^{y+1}+y^{x+1} is (y^x+x)(x^y+y)

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factor x^yy^x+xy+x^{y+1}+y^{x+1}

factor

x^{y} y^{x} + x y + x^{y + 1} + y^{x + 1}

(y^{x} + x) (x^{y} + y)

Solution steps

x^{y} y^{x} + x y + x^{y + 1} + y^{x + 1}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= x^{y} y^{x} + x y + x^{1} x^{y} + y^{1} y^{x}

Factor out common term

x^{y}

= x^{y} (y^{x} + x) + x y + y^{x} y

Factor out common term

y

= x^{y} (y^{x} + x) + y (x + y^{x})

Factor out common term

(y^{x} + x)

= (y^{x} + x) (x^{y} + y)

9 v (2 v + 7) - 12 v (2 v + 7)

9 k^{4} - 1 2^{2} m + 4 m^{2}

3 ab - 3 b + 4 c - 4 a c

6 b^{x - 2} - 4 b^{x + 2}

[- 10.7]

What is factor x^yy^x+xy+x^{y+1}+y^{x+1} ?
The solution to factor x^yy^x+xy+x^{y+1}+y^{x+1} is (y^x+x)(x^y+y)