Question

Suppose that \Join is an operation defined by x Join y = (x+2)(y-3). What is (t) \Join (t+2) - (t+1) \Join (t+1)?

Answer 1

The expression for (t) \Join (t+2) - (t+1) \Join (t+1) is ( $t^{2}$ + t - 2 ) ( $t^{2}$ + t - 6 ).

The given operation is \Join such that x Join y = (x+2)(y-3).

We are to apply the \Join operation in the given expression.

t \join (t+2) - (t+1) \Join (t+1) and find its final expression.

Using this operation: x Join y = (x+2)(y-3).

Let's find,

t \join (t+2)

Here,

x = t and y = t + 2

= ( t+2 ) ( t+2 - 3 )

= ( t + 2 ) ( t - 1 )

(t+1) \Join (t+1)

Here,

x = t + 1 and y = t + 1

= ( t + 1 + 2 ) ( t + 1 - 3 )

= ( t + 3 ) ( t - 2 )

t \join (t+2) - (t+1) \Join (t+1)

= ( t + 2 ) ( t - 1 ) - ( t + 3 ) ( t - 2 )

= ( $t^{2}$ - t + 2t - 2 ) ( $t^{2}$ - 2t + 3t - 6 )

= ( $t^{2}$ + t - 2 ) ( $t^{2}$ + t - 6 )

Thus the expression for (t) \Join (t+2) - (t+1) \Join (t+1) is:

( $t^{2}$ + t - 2 ) ( $t^{2}$ + t - 6 )

Learn more about mathematical operation here:

brainly.com/question/27915566

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