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When we multiply them, we distribute each term in the first polynomial to each term in the second polynomial, like so:

(x+1)(x+2)

=x(x+2) + 1(x+2)

=x2 + 2x + x + 2

=x2 + 3x + 2.

The green grass. A white cloud with an outline. A white cloud with an outline. Parentheses with x plus 1 inside. Parentheses with x plus 2 inside.