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Algebra
Advanced Factorization
Excel in math and science
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If \(x-y-5=0\), then the polynomial \[3x^2+xy-y^2-25x-y+50\] can be simplified as \(ay(y+b)\). What is \(a+b\)?
Excel in math and science
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Given that \[\begin{align} & x = -a+b+c, \\ & y = a-b+c, \\ & z = a+b-c ,\\ & a^2+b^2+c^2 =20, \end{align}\] find the value of \(x^2+y^2+z^2+xy+yz+zx\).
Excel in math and science
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Suppose that \(a\) is an integer such that \[x^2+2xy-80y^2+ax+18y+81\] can be factorized as the product of linear expressions in \(x\) and \(y\). What is the value of \(a\)?
Excel in math and science
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\(a, b\) and \(c \) are integers such that \[ (x-a)(x-20) + 1 = (x+b)(x+c) .\] What is the sum of all possible values of \( a \)?
Excel in math and science
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Suppose \(a\), \(b\) and \(c\) are real numbers such that \[a+b+c=5.\] If \[x=a-2b+3c, y=b-2c+3a, z=c-2a+3b,\] what is the value of \[(x^2+2xy+4)+(y^2+2yz+4)+(z^2+2zx+4)?\]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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by Brilliant Staff