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Question

Resolve each of the following quadratic trinomial into factor:
15x2 − 16xyz − 15y2z2

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Solution

The given expression is 15x2-16xyz-15y2z2.(Coefficient of x2=15, coefficient of x=-16yz and constant term=-15y2z2)Now, we will split the coefficient of x into two parts such that their sum is -16yz and their product equals the product of the coefficient of x2 and the constant term, i.e., 15×(-15y2z2)=-225y2z2.Now,(-25yz)+9yz=-16yx and (-25yz)×9yz=-225y2z2Replacing the middle term -16xyz by -25xyz+9xyz, we have:15x2-16xyz-15y2z2=15x2-25xyz+9xyz-15y2z2 =(15x2-25xyz)+(9xyz-15y2z2) =5x(3x-5yz)+3yz(3x-5yz) =(5x+3yz)(3x-5yz)

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