What is factor 9a^{6m}-16b^{4n} ?

The solution to factor 9a^{6m}-16b^{4n} is (3a^{3m}+4b^{2n})(3a^{3m}-4b^{2n})

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factor 9a^{6m}-16b^{4n}

factor

9 a^{6 m} - 16 b^{4 n}

(3 a^{3 m} + 4 b^{2 n}) (3 a^{3 m} - 4 b^{2 n})

Solution steps

9 a^{6 m} - 16 b^{4 n}

Rewrite

9 a^{6 m}

(3 a^{3 m})^{2}

Rewrite

16 b^{4 n}

(2 b^{1 n})^{4}

= (3 a^{3 m})^{2} - (2 b^{1 \cdot n})^{4}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

(2 b^{1 n})^{4} = ((2 b^{1 n})^{2})^{2}

= (3 a^{3 m})^{2} - ((2 b^{1 n})^{2})^{2}

Apply Difference of Two Squares Formula:

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

(3 a^{3 m})^{2} - ((2 b^{1 n})^{2})^{2} = (3 a^{3 m} + (2 b^{1 n})^{2}) (3 a^{3 m} - (2 b^{1 n})^{2})

= (3 a^{3 m} + (2 b^{1 n})^{2}) (3 a^{3 m} - (2 b^{1 n})^{2})

Simplify

(3 a^{3 m} + (2 b^{1 \cdot n})^{2}) (3 a^{3 m} - (2 b^{1 \cdot n})^{2}) : (3 a^{3 m} + 4 b^{2 n}) (3 a^{3 m} - 4 b^{2 n})

= (3 a^{3 m} + 4 b^{2 n}) (3 a^{3 m} - 4 b^{2 n})

(7 x^{2}) - 6

(5 a + 4) - (5 a + 3)^{'}

m r + n s + n r + m s

(3 - 3 i)^{\frac{1}{2}}

a^{(2)} + 11 x + 35

What is factor 9a^{6m}-16b^{4n} ?
The solution to factor 9a^{6m}-16b^{4n} is (3a^{3m}+4b^{2n})(3a^{3m}-4b^{2n})