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Factorise: 4x^2-4xy-3y^2+12yz-9z^2​

User Lczapski
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To factorize the expression
4x^(2) - 4xy - 3y^(2) + 12yz - 9z^2, you can first look for common factors in pairs of terms. In this case, you can factor by grouping:


4x^2-4xy-3y^2+12yz-9z^2=(4x^2-4xy-3y^2+(12yz-9z^2)

Now, let's factor each of these groups separately:

For the first group,
4x^2-4xy-3y^2, you can factor it as follows:


4x^2 - 4xy - 3y^2 = (4x^2 - 6xy+2xy-3y^2)=2x(2x-3y)-1(2x-3y)=(2x-1)(2x-3y)

For the second group,
12yz-9z^2, you can factor out the common factor of 3z:


12yz - 9z^2 = 3z(4y-3z)

Now, you have factored in both groups:


4x^2-4xy-3y^2+12yz-9z^2=(2x-1)(2x-3y)+3z(4y-3z)\\

So, the fully factorized expression is
(2x-1)(2x-3y)+3z(4y-3z)

User Hrvoje T
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