x+2y^ 2-4(2x-y) ^2 factorise
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Answer:
How to solve your question
Your question is
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(x-2y)^{2}-1(2x+y)^{2}
(x−2y)2−1(2x+y)2
Simplify
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Expand the square
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(x-2y)^{2}-1(2x+y)^{2}
(x−2y)2−1(2x+y)2
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(x-2y)(x-2y)-1(2x+y)^{2}
(x−2y)(x−2y)−1(2x+y)2
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Distribute
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{\color{#c92786}{(x-2y)(x-2y)}}-1(2x+y)^{2}
(x−2y)(x−2y)−1(2x+y)2
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{\color{#c92786}{x(x-2y)-2y(x-2y)}}-1(2x+y)^{2}
x(x−2y)−2y(x−2y)−1(2x+y)2
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Distribute
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{\color{#c92786}{x(x-2y)-2y(x-2y)}}-1(2x+y)^{2}
x(x−2y)−2y(x−2y)−1(2x+y)2
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Distribute
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{\color{#c92786}{x(x-2y)}}-2y(x-2y)-1(2x+y)^{2}
x(x−2y)−2y(x−2y)−1(2x+y)2
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{\color{#c92786}{x^{2}-2xy}}-2y(x-2y)-1(2x+y)^{2}
x2−2xy−2y(x−2y)−1(2x+y)2
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Distribute
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x^{2}-2xy{\color{#c92786}{-2y(x-2y)}}-1(2x+y)^{2}
x2−2xy−2y(x−2y)−1(2x+y)2
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x^{2}-2xy{\color{#c92786}{-2xy+4y^{2}}}-1(2x+y)^{2}
x2−2xy−2xy+4y2−1(2x+y)2
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Combine like terms
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x^{2}{\color{#c92786}{-2xy}}{\color{#c92786}{-2xy}}+4y^{2}-1(2x+y)^{2}
x2−2xy−2xy+4y2−1(2x+y)2
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x^{2}{\color{#c92786}{-4xy}}+4y^{2}-1(2x+y)^{2}
x2−4xy+4y2−1(2x+y)2
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