What is factor 100x^{2a-2b}-49y^{4c} ?

The solution to factor 100x^{2a-2b}-49y^{4c} is (10x^{a-b}+7y^{2c})(10x^{a-b}-7y^{2c})

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factor 100x^{2a-2b}-49y^{4c}

factor

100 x^{2 a - 2 b} - 49 y^{4 c}

(10 x^{a - b} + 7 y^{2 c}) (10 x^{a - b} - 7 y^{2 c})

Solution steps

100 x^{2 a - 2 b} - 49 y^{4 c}

x^{2 a - 2 b} = x^{2 (a - b)}

= 100 x^{2 (a - b)} - 49 y^{4 c}

Rewrite

100 x^{2 (a - b)}

(10 x^{1 (a - b)})^{2}

Rewrite

49 y^{4 c}

(7 y^{2 c})^{2}

= (10 x^{1 \cdot (a - b)})^{2} - (7 y^{2 c})^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(10 x^{1 (a - b)})^{2} - (7 y^{2 c})^{2} = (10 x^{1 (a - b)} + 7 y^{2 c}) (10 x^{1 (a - b)} - 7 y^{2 c})

= (10 x^{1 (a - b)} + 7 y^{2 c}) (10 x^{1 (a - b)} - 7 y^{2 c})

Refine

= (10 x^{a - b} + 7 y^{2 c}) (10 x^{a - b} - 7 y^{2 c})

- 4 - (\frac{- 3 + 41}{2})

1 - (2 x)

m x - m y + m z + n x - n y + n z

3 a x - 6 a y - 8 b y + 4 b x

2 + (a + b)

What is factor 100x^{2a-2b}-49y^{4c} ?
The solution to factor 100x^{2a-2b}-49y^{4c} is (10x^{a-b}+7y^{2c})(10x^{a-b}-7y^{2c})