Factor (2c^2-3cy+y^2)(c^2+4cy-3y^2)

Math
(2c2-3cy+y2)(c2+4cy-3y2)
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅1=2 and whose sum is b=-3.
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Reorder terms.
(2c2+y2-3cy)(c2+4cy-3y2)
Reorder y2 and -3cy.
(2c2-3cy+y2)(c2+4cy-3y2)
Factor -3 out of -3cy.
(2c2-3(cy)+y2)(c2+4cy-3y2)
Rewrite -3 as -1 plus -2
(2c2+(-1-2)(cy)+y2)(c2+4cy-3y2)
Apply the distributive property.
(2c2-1(cy)-2(cy)+y2)(c2+4cy-3y2)
Remove unnecessary parentheses.
(2c2-1cy-2(cy)+y2)(c2+4cy-3y2)
Remove unnecessary parentheses.
(2c2-1cy-2cy+y2)(c2+4cy-3y2)
(2c2-1cy-2cy+y2)(c2+4cy-3y2)
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
((2c2-1cy)-2cy+y2)(c2+4cy-3y2)
Factor out the greatest common factor (GCF) from each group.
(c(2c-1y)-y(2c-y))(c2+4cy-3y2)
(c(2c-1y)-y(2c-y))(c2+4cy-3y2)
Factor the polynomial by factoring out the greatest common factor, 2c-1y.
(2c-1y)(c-y)(c2+4cy-3y2)
(2c-1y)(c-y)(c2+4cy-3y2)
Rewrite -1y as -y.
(2c-y)(c-y)(c2+4cy-3y2)
Factor (2c^2-3cy+y^2)(c^2+4cy-3y^2)

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