(A) To expand the expression $(x+2t)(x-5t)$,we use the algebraic identity $(x+a)(x+b) = x^2 + (a+b)x + ab$.Here,$a = 2t$ and $b = -5t$.Substituting th

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(A) To expand the expression $(x+2t)(x-5t)$,we use the algebraic identity $(x+a)(x+b) = x^2 + (a+b)x + ab$.Here,$a = 2t$ and $b = -5t$.Substituting these values into the identity:$(x+2t)(x-5t) = x^2 + (2t - 5t)x + (2t)(-5t)$$= x^2 + (-3t)x - 10t^2$$= x^2 - 3xt - 10t^2$.