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Popular >

factor a^{3y}+1

Solution

factor

a^{3 y} + 1

Solution

(a^{y} + 1) (a^{2 y} - a^{y} + 1)

Solution steps

a^{3 y} + 1

Apply exponent rule:

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

a^{3 y} = (a^{y})^{3}

= (a^{y})^{3} + 1

Rewrite

1

as

1^{3}

= (a^{y})^{3} + 1^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(a^{y})^{3} + 1^{3} = (a^{y} + 1) ((a^{y})^{2} - a^{y} + 1)

= (a^{y} + 1) ((a^{y})^{2} - a^{y} + 1)

Simplify

(a^{y} + 1) ((a^{y})^{2} - a^{y} + 1) : (a^{y} + 1) (a^{2 y} - a^{y} + 1)

= (a^{y} + 1) (a^{2 y} - a^{y} + 1)

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Frequently Asked Questions (FAQ)

What is factor a^{3y}+1 ?
The solution to factor a^{3y}+1 is (a^y+1)(a^{2y}-a^y+1)