rút gọn: a, -3x(x+2) ² + (x+3) (x-1) (x+1) – (2x-3) ² b, (x+5) ² -4x(2x+3) ² -(2x-1)(x+3)(x-3) 22/07/2021 Bởi Parker rút gọn: a, -3x(x+2) ² + (x+3) (x-1) (x+1) – (2x-3) ² b, (x+5) ² -4x(2x+3) ² -(2x-1)(x+3)(x-3)
Đáp án: Giải thích các bước giải: Áp dụng các hằng đẳng thức : $(A+B)^2=A^2+2AB+B^2$ $(A-B)^2=A^2-2AB+B^2$ $(A^2-B^2=(A-B)(A+B)$ $a) -3x(x + 2) ² + (x + 3)(x – 1)(x + 1) – (2x – 3) ²$ $= -3x(x² + 4x + 4) + (x + 3)(x² – 1) – (4x² – 12x + 9)$ $= -3x³ – 12x² – 12x + x³ – x + 3x² – 3 – 4x² + 12x – 9$ $= -2x³ – 13x² – x – 12 $ $b)(x+5) ² -4x(2x+3) ² -(2x-1)(x+3)(x-3)$ $= x² + 10x + 25 – 4x(4x² + 12x + 9) – (2x – 1)(x² – 9)$ $= x² + 10x + 25 – 16x³ – 48x² – 36x – 2x³ + 18x + x² – 9$ $= -18x³ – 46x² – 8x + 16$ Bình luận
a, -3x(x + 2) ² + (x + 3)(x – 1)(x + 1) – (2x – 3) ² = -3x(x² + 4x + 4) + (x + 3)(x² – 1) – (4x² – 12x + 9) = -3x³ – 12x² – 12x + x³ – x + 3x² – 3 – 4x² + 12x – 9 = -2x³ – 13x² – x – 12 b, (x+5) ² -4x(2x+3) ² -(2x-1)(x+3)(x-3) = x² + 10x + 25 – 4x(4x² + 12x + 9) – (2x – 1)(x² – 9) = x² + 10x + 25 – 16x³ – 48x² – 36x – 2x³ + 18x + x² – 9 = -18x³ – 46x² – 8x + 16 Bình luận
Đáp án:
Giải thích các bước giải:
Áp dụng các hằng đẳng thức :
$(A+B)^2=A^2+2AB+B^2$
$(A-B)^2=A^2-2AB+B^2$
$(A^2-B^2=(A-B)(A+B)$
$a) -3x(x + 2) ² + (x + 3)(x – 1)(x + 1) – (2x – 3) ²$
$= -3x(x² + 4x + 4) + (x + 3)(x² – 1) – (4x² – 12x + 9)$
$= -3x³ – 12x² – 12x + x³ – x + 3x² – 3 – 4x² + 12x – 9$
$= -2x³ – 13x² – x – 12 $
$b)(x+5) ² -4x(2x+3) ² -(2x-1)(x+3)(x-3)$
$= x² + 10x + 25 – 4x(4x² + 12x + 9) – (2x – 1)(x² – 9)$
$= x² + 10x + 25 – 16x³ – 48x² – 36x – 2x³ + 18x + x² – 9$
$= -18x³ – 46x² – 8x + 16$
a, -3x(x + 2) ² + (x + 3)(x – 1)(x + 1) – (2x – 3) ²
= -3x(x² + 4x + 4) + (x + 3)(x² – 1) – (4x² – 12x + 9)
= -3x³ – 12x² – 12x + x³ – x + 3x² – 3 – 4x² + 12x – 9
= -2x³ – 13x² – x – 12
b, (x+5) ² -4x(2x+3) ² -(2x-1)(x+3)(x-3)
= x² + 10x + 25 – 4x(4x² + 12x + 9) – (2x – 1)(x² – 9)
= x² + 10x + 25 – 16x³ – 48x² – 36x – 2x³ + 18x + x² – 9
= -18x³ – 46x² – 8x + 16