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Factor the expression completely.

x^(5)y^(5)+xy^(4)
Answer:

Factor the expression completely.\newlinex5y5+xy4 x^{5} y^{5}+x y^{4} \newlineAnswer:

Full solution

Q. Factor the expression completely.\newlinex5y5+xy4 x^{5} y^{5}+x y^{4} \newlineAnswer:
  1. Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression x5y5x^{5}y^{5} and xy4xy^{4}. The GCF is xy4xy^{4} because it is the highest degree of xx and yy that divides both terms.
  2. Factor out GCF: Factor out the GCF from the expression.\newlinex5y5+xy4=xy4(x4y+1)x^{5}y^{5} + xy^{4} = xy^{4}(x^{4}y + 1)\newlineWe divide each term by xy4xy^{4} to find the remaining factors.
  3. Divide terms: Check the factored expression to ensure that when the GCF is distributed back into the parentheses, we get the original expression.\newlinexy4(x4y+1)=xy4×x4y+xy4×1=x5y5+xy4xy^{4}(x^{4}y + 1) = xy^{4} \times x^{4}y + xy^{4} \times 1 = x^{5}y^{5} + xy^{4}\newlineThe original expression is obtained, so there is no math error.

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