Question

factorise this fast

x^4 - 81y^4

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Answer 1

Heya!⭐

Solution:

${x}^{4} - 81 {y}^{4}$

$( { {x}^{2} )}^{2} - ({ {9y}^{2} })^{2}$

${x}^{2} - ( {3y}^{2} )( {x}^{2} + {9y}^{2} )$

$(x - 3y)(x + 3y)( {x}^{2} + {9y}^{2})$

Hope this helps

@adiba31✌❤️

Answer 2

Answer:

Rewrite x4x4 as (x2)2(x2)2.

(x2)2−81y4(x2)2-81y4

Rewrite 81y481y4 as (9y2)2(9y2)2.

(x2)2−(9y2)2(x2)2-(9y2)2

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=x2a=x2 and b=9y2b=9y2.

(x2+9y2)(x2−(9y2))(x2+9y2)(x2-(9y2))

Simplify.

(x2+9y2)(x2−(9y2)

Rewrite 9y29y2 as (3y)2(3y)2.

(x2+9y2)(x2−(3y)2)(x2+9y2)(x2-(3y)2)

Since both terms are perfect squares, factorusing the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=xa=x and b=3yb=3y.

(x2+9y2)((x+3y)(x−(3y)))

Multiply 33 by −1-1.

(x2+9y2)((x+3y)(x−3y))(x2+9y2)((x+3y)(x-3y))

Remove unnecessary parentheses.

(x2+9y2)(x+3y)(x−3y)