What is factor a^{x+y}+a^xb^y-a^yb^x-b^{x+y} ?

The solution to factor a^{x+y}+a^xb^y-a^yb^x-b^{x+y} is (a^y+b^y)(a^x-b^x)

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factor a^{x+y}+a^xb^y-a^yb^x-b^{x+y}

factor

a^{x + y} + a^{x} b^{y} - a^{y} b^{x} - b^{x + y}

(a^{y} + b^{y}) (a^{x} - b^{x})

Solution steps

a^{x + y} + a^{x} b^{y} - a^{y} b^{x} - b^{x + y}

Apply exponent rule:

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

= a^{y} a^{x} + a^{x} b^{y} - a^{y} b^{x} - b^{y} b^{x}

Factor out common term

a^{x}

= a^{x} (a^{y} + b^{y}) - a^{y} b^{x} - b^{x} b^{y}

Factor out common term

b^{x}

= a^{x} (a^{y} + b^{y}) - b^{x} (a^{y} + b^{y})

Factor out common term

(a^{y} + b^{y})

= (a^{y} + b^{y}) (a^{x} - b^{x})

15 x^{2} - 11 x - 12

4 = 3 a - 14

0.05 (x + 6) + 0.1 (x) = 1.8

x^{2} - 10 + 21

- 1.2 > \frac{x}{- 5}

What is factor a^{x+y}+a^xb^y-a^yb^x-b^{x+y} ?
The solution to factor a^{x+y}+a^xb^y-a^yb^x-b^{x+y} is (a^y+b^y)(a^x-b^x)