To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
(color(red)(x^2) + color(red)(5x) - color(red)(1))(color(blue)(5x^2) - color(blue)(6x) + color(blue)(1))(x2+5x−1)(5x2−6x+1) becomes:
(color(red)(x^2) xx color(blue)(5x^2)) - (color(red)(x^2) xx color(blue)(6x)) + (color(red)(x^2) xx color(blue)(1)) + (color(red)(5x) xx color(blue)(5x^2)) - (color(red)(5x) xx color(blue)(6x)) + (color(red)(5x) xx color(blue)(1)) - (color(red)(1) xx color(blue)(5x^2)) + (color(red)(1) xx color(blue)(6x)) - (color(red)(1) xx color(blue)(1))(x2×5x2)−(x2×6x)+(x2×1)+(5x×5x2)−(5x×6x)+(5x×1)−(1×5x2)+(1×6x)−(1×1)
5x^4 - 6x^3 + x^2 + 25x^3 - 30x^2 + 5x - 5x^2 + 6x - 15x4−6x3+x2+25x3−30x2+5x−5x2+6x−1
We can now group and combine like terms:
5x^4 - 6x^3 + 25x^3 + x^2 - 30x^2 - 5x^2 + 5x + 6x - 15x4−6x3+25x3+x2−30x2−5x2+5x+6x−1
5x^4 + (-6 + 25)x^3 + (1 - 30 - 5)x^2 + (5 + 6)x - 15x4+(−6+25)x3+(1−30−5)x2+(5+6)x−1
5x^4 + 19x^3 - 34x^2 + 11x - 15x4+19x3−34x2+11x−1
