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Factor completely: (4x+7)^(2)+(4x+7)^(3) Answer:

Factor completely:\newline(4x+7)2+(4x+7)3 (4 x+7)^{2}+(4 x+7)^{3} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(4x+7)2+(4x+7)3 (4 x+7)^{2}+(4 x+7)^{3} \newlineAnswer:
  1. Recognize common factor: Recognize the common factor in both terms.\newlineThe expression given is (4x+7)2+(4x+7)3(4x+7)^{2}+(4x+7)^{3}. We can see that (4x+7)(4x+7) is a common factor in both terms.
  2. Factor out common factor: Factor out the common factor.\newlineWe can factor out (4x+7)(4x+7) from both terms, which gives us:\newline(4x+7)((4x+7)1+(4x+7)2)(4x+7)((4x+7)^{1}+(4x+7)^{2})
  3. Simplify inside parentheses: Simplify the expression inside the parentheses.\newlineNow we simplify the expression inside the parentheses by adding the exponents:\newline(4x+7)(1×(4x+7)1+1×(4x+7)2)(4x+7)(1\times(4x+7)^{1} + 1\times(4x+7)^{2})\newline= (4x+7)(4x+7+(4x+7)2)(4x+7)(4x+7 + (4x+7)^{2})
  4. Recognize no further simplification: Recognize that the expression inside the parentheses cannot be simplified further.\newlineThe expression 4x+7+(4x+7)24x+7 + (4x+7)^{2} does not have any common factors or like terms that can be combined, so it is already in its simplest form.
  5. Write final factored form: Write the final factored form.\newlineThe completely factored form of the expression is:\newline(4x+7)(1+(4x+7)+(4x+7)2)(4x+7)(1 + (4x+7) + (4x+7)^{2})

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