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Expanding two brackets multiplies every term in the first by every term in the second — the FOIL pattern. The x coefficient is the sum of the two cross products ad + bc.
Expanding
(ax + b)(cx + d) = acx² + (ad + bc)x + bd
12x² + 15x − 8x − 10 = 12x² + 7x − 10.
First, Outer, Inner, Last — the four products you form, though the underlying rule is just the distributive law.