Factorise 9x^2y-24xy^2+16y^3

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Solution

9x²y-24xy²+16y³ Final result : y • (3x - 4y)² Step by step solution : Step1: Equation at the end of step1: (((9•(x²))•y)-(24x•(y²)))+2⁴y³ Step 2 : Equation at the end of step2: (((9 • (x²)) • y) - (2³•3xy²)) + 2⁴y³ Step 3 : Equation at the end of step3: ((3²x² • y) - (2³•3xy²)) + 2⁴y³ Step4: Step5: Pulling out like terms :
5.1 Pull out like factors: 9x²y - 24xy²+ 16y³=y•(9x²- 24xy + 16y²)
Trying to factor a multi variable polynomial :
5.2 Factoring9x²- 24xy + 16y² Try to factor this multi-variable trinomial using trial and error Found a factorization:(3x - 4y)•(3x - 4y)
Detecting a perfect square :
5.39x²-24xy+16y² is a perfect square It factors into(3x-4y)•(3x-4y) which is another way of writing(3x-4y)² How to recognize a perfect square trinomial: • It has three terms • Two of its terms are perfect squares themselves • The remaining term is twice the product of the square roots of the other two terms
Final result : y • (3x - 4y)²

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