Factor the trinomial completely. \[ x^{2}+13 x y+40 y^{2} \] Select the correct choice below and, if necessary, fill in the answer box A. \( x^{2}+13 x y+40 y^{2}=\square \) B. The trinomial is pnme.

Factor the expression \( x^{2}+13x*y+40y^{2} \). Factor the expression by following steps: - step0: Factor: \(x^{2}+13xy+40y^{2}\) - step1: Rewrite the expression: \(x^{2}+\left(5+8\right)xy+40y^{2}\) - step2: Calculate: \(x^{2}+5xy+8yx+40y^{2}\) - step3: Rewrite the expression: \(x\times x+x\times 5y+8yx+8y\times 5y\) - step4: Factor the expression: \(x\left(x+5y\right)+8y\left(x+5y\right)\) - step5: Factor the expression: \(\left(x+8y\right)\left(x+5y\right)\) The trinomial \(x^{2}+13xy+40y^{2}\) can be factored completely as \((x+8y)(x+5y)\). Therefore, the correct choice is: A. \(x^{2}+13xy+40y^{2}=(x+8y)(x+5y)\)