1. (10 points) Consider the set V of polynomials of the form ac® + bx4+ca² +d, where a, b, c, d e R. Verify that for X, Y E V and A, y ER we have the following identities: (i) X(X +Y) = \X + XY (ii) (A + v)X = AX +yX

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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1. (10 points) Consider the set V of polynomials of the form ax®+bxª +cx² +d, where a, b, c, d e R.
Verify that for X, Y E V and A, y e R we have the following identities:
(i) X(X +Y) = AX + XY
(ii) (A + v)X = AX +yX
Transcribed Image Text:1. (10 points) Consider the set V of polynomials of the form ax®+bxª +cx² +d, where a, b, c, d e R. Verify that for X, Y E V and A, y e R we have the following identities: (i) X(X +Y) = AX + XY (ii) (A + v)X = AX +yX
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