factorise 50(x+y)²-18(x-y)²
Answers
Answer:
8(4x+y)(x+4y)
Step-by-step explanation:
50(x+y)2−18(x−y)250(x+y)2-18(x-y)2
Factor 22 out of 50(x+y)2−18(x−y)250(x+y)2-18(x-y)2.
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2(25(x+y)2−9(x−y)2)2(25(x+y)2-9(x-y)2)
Rewrite 25(x+y)225(x+y)2 as (5(x+y))2(5(x+y))2.
2((5(x+y))2−9(x−y)2)2((5(x+y))2-9(x-y)2)
Rewrite 9(x−y)29(x-y)2 as (3(x−y))2(3(x-y))2.
2((5(x+y))2−(3(x−y))2)2((5(x+y))2-(3(x-y))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=5(x+y)a=5(x+y) and b=3(x−y)b=3(x-y).
2((5(x+y)+3(x−y))(5(x+y)−(3(x−y))))2((5(x+y)+3(x-y))(5(x+y)-(3(x-y))))
Factor.
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2⋅2(4x+y)(5(x+y)−3(x−y))2⋅2(4x+y)(5(x+y)-3(x-y))
Multiply 2 by 2.
4(4x+y)(5(x+y)−3(x−y))4(4x+y)(5(x+y)-3(x-y))
Apply the distributive property.
4(4x+y)(5x+5y−3(x−y))4(4x+y)(5x+5y-3(x-y))
Apply the distributive property.
4(4x+y)(5x+5y−3x−3(−y))4(4x+y)(5x+5y-3x-3(-y))
Multiply −1-1 by −3-3.
4(4x+y)(5x+5y−3x+3y)4(4x+y)(5x+5y-3x+3y)
Subtract 3x3x from 5x5x.
4(4x+y)(2x+5y+3y)4(4x+y)(2x+5y+3y)
Add 5y5y and 3y3y.
4(4x+y)(2x+8y)4(4x+y)(2x+8y)
Factor.
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4(4x+y)⋅2(x+4y)4(4x+y)⋅2(x+4y)
Multiply 22 by 44.
8(4x+y)(x+4y)
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Step-by-step explanation:
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