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Answer :
Final answer:
The expression 15x⁴ + 15x²y³ + 20x³y + 20xy⁴ can be factored out by first factoring out the GCF (5x²) then using the factoring by grouping method resulting in 5x²(y(3x+3y)+4y(x+y)).
Explanation:
The problem involves factoring out the Greatest Common Factor (GCF) first and then factoring by grouping. The expression given is 15x⁴ + 15x²y³ + 20x³y + 20xy⁴. The first step to solve this is find the GCF. Here it is 5x² (the smallest power of x and factor of all coefficients). When we factor out the GCF from each term, the expression simplifies to 5x²(3x²+3y³+4xy+4y⁴).
Secondly, we factor it by grouping. In our simplified expression, we can group 3x²+3y³ together and 4xy+4y⁴ together. Factoring those groups separately gives 5x²(y(3x+3y)+4y(x+y)). Thus, 15x⁴ + 15x²y³ + 20x³y + 20xy⁴ = 5x²(y(3x+3y)+4y(x+y))
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