12. Упростите выражение: 1) (x + 2)(x - 5) - 3x(1 - 2x); 2) (x - 2)(x - 11) - 2x(4 - 3x); 3) (a + 6)(a - 3) + (a - 4)(a + 5); 4) (a + 3)(a - 2) + (a - 3)(a + 6).

Question

Вопрос:

Accepted Answer

\( (x+2)(x-5) - 3x(1-2x) = (x^2 - 5x + 2x - 10) - (3x - 6x^2) = x^2 - 3x - 10 - 3x + 6x^2 = (x^2 + 6x^2) + (-3x - 3x) - 10 = 7x^2 - 6x - 10 \)
\( (x-2)(x-11) - 2x(4-3x) = (x^2 - 11x - 2x + 22) - (8x - 6x^2) = x^2 - 13x + 22 - 8x + 6x^2 = (x^2 + 6x^2) + (-13x - 8x) + 22 = 7x^2 - 21x + 22 \)
\( (a+6)(a-3) + (a-4)(a+5) = (a^2 - 3a + 6a - 18) + (a^2 + 5a - 4a - 20) = (a^2 + 3a - 18) + (a^2 + a - 20) = a^2 + 3a - 18 + a^2 + a - 20 = (a^2 + a^2) + (3a + a) + (-18 - 20) = 2a^2 + 4a - 38 \)
\( (a+3)(a-2) + (a-3)(a+6) = (a^2 - 2a + 3a - 6) + (a^2 + 6a - 3a - 18) = (a^2 + a - 6) + (a^2 + 3a - 18) = a^2 + a - 6 + a^2 + 3a - 18 = (a^2 + a^2) + (a + 3a) + (-6 - 18) = 2a^2 + 4a - 24 \)

Ответ: 1) 7x² - 6x - 10; 2) 7x² - 21x + 22; 3) 2a² + 4a - 38; 4) 2a² + 4a - 24.