Question 268764: -yw-6w+3y^2+18y
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! (100xy-25y)/(5x)+(4x^(2)-18y^(2))/(6y)
=►Factor out the GCF of 25y from each term in the polynomial.
(25y(4x)+25y(-1))/(5x)+(4x^(2)-18y^(2))/(6y)
=►Factor out the GCF of 25y from 100xy-25y.
(25y(4x-1))/(5x)+(4x^(2)-18y^(2))/(6y)
=►Reduce the expression (25y(4x-1))/(5x) by removing a factor of 5 from the numerator and denominator.
(5y(4x-1))/(x)+(4x^(2)-18y^(2))/(6y)
=►Factor out the GCF of 2 from each term in the polynomial.
(5y(4x-1))/(x)+(2(2x^(2))+2(-9y^(2)))/(6y)
=►Factor out the GCF of 2 from 4x^(2)-18y^(2).
(5y(4x-1))/(x)+(2(2x^(2)-9y^(2)))/(6y)
=►Reduce the expression (2(2x^(2)-9y^(2)))/(6y) by removing a factor of 2 from the numerator and denominator.
(5y(4x-1))/(x)+(2x^(2)-9y^(2))/(3y)
=►Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 3xy. The (5y(4x-1))/(x) expression needs to be multiplied by ((3y))/((3y)) to make the denominator 3xy. The ((2x^(2)-9y^(2)))/(3y) expression needs to be multiplied by ((x))/((x)) to make the denominator 3xy.
(5y(4x-1))/(x)*(3y)/(3y)+(2x^(2)-9y^(2))/(3y)*(x)/(x)
=►Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3xy.
(5y(4x-1)(3y))/(3xy)+(2x^(2)-9y^(2))/(3y)*(x)/(x)
=►Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3xy.
(5y(4x-1)(3y))/(3xy)+((2x^(2)-9y^(2))(x))/(3xy)
=►The numerators of expressions that have equal denominators can be combined. In this case, (5y(4x-1)(3y))/(3xy) and (((2x^(2)-9y^(2))(x)))/(3xy) have the same denominator of 3xy, so the numerators can be combined.
(5y(4x-1)(3y)+((2x^(2)-9y^(2))(x)))/(3xy)
=►Simplify the numerator of the expression.
Answer: (51xy^(2)+2x^(3)-15y^(2))/(3xy)
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