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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$
Learn how to solve simplification of algebraic fractions problems step by step online.
$derivdef\left(\frac{\left(2x+3y\right)\left(4x^{2}-6xy+9y^{2}\right)}{2x+3y}\right)$
Learn how to solve simplification of algebraic fractions problems step by step online. Find the derivative of (8x^3+27y^3)/(2x+3y) using the definition. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Simplify the fraction \frac{\left(2x+3y\right)\left(4x^{2}-6xy+9y^{2}\right)}{2x+3y} by 2x+3y. Find the derivative of 4x^{2}-6xy+9y^{2} using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 4x^{2}-6xy+9y^{2}. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(4x^{2}-6xy+9y^{2}\right).