# Find the HCF from x^3 - 8y^3 and x^2 + 4x^(2)y^(2) + 16y^4

can someone pls help me to find the hcf

Go to main content# Find the HCF from x^3 - 8y^3 and x^2 + 4x^(2)y^(2) + 16y^4

can someone pls help me to find the hcf

1st expression: x^3 - 8y^3

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

= (x - 2y)(x^{2} + 2xy + 4y^{2})

2nd expression: x^{2} + 4x^{2}y^{2} + 16y^{4}

= x^{2} + (4y^{2})^{2} + 4x^{2}y^{2}

= (x + 4y^{2})^{2} - 8x^{2}y^{2} + 4x^{2}y^{2}

= (x + 4y^{2})^{2} - (2xy)^{2}

= (x + 4y^{2} + 2xy)(x + 4y^{2} - 2xy)

= (x + 2xy + 4y^{2})(x - 2xy + 4y^{2})

From above, we can find that the highest common factor (HCF) is (x + 2xy + 4y^{2})

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