factorise x^4-6x^2y^2+9y^4-81
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Heya User,
I've used -->
--> a² - 2ab + b² = (a-b)²
--> a² - b² = (a+b)(a-b)
--> [tex]x^4 - 6x^2y^2 + 9y^4 - 81 \\ = x^4 - 2(3y^2)x^2 + (3y^2)^2 - 81 \\ = [ x^2 - 3y^2 ]^2 - 9^2 \\ = [ x^2 - 3y^2 + 9 ][ x^2 - 3y^2 - 9 ][/tex]
There you go...
I've used -->
--> a² - 2ab + b² = (a-b)²
--> a² - b² = (a+b)(a-b)
--> [tex]x^4 - 6x^2y^2 + 9y^4 - 81 \\ = x^4 - 2(3y^2)x^2 + (3y^2)^2 - 81 \\ = [ x^2 - 3y^2 ]^2 - 9^2 \\ = [ x^2 - 3y^2 + 9 ][ x^2 - 3y^2 - 9 ][/tex]
There you go...
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