Môn Toán Lớp 8: Rút gọn bt `1, (2x 1)2 (x -5)2 - 5x (x -4)` `2, (3x 2)2 - (3x - 1) (3x 1)` `3, (5x 2)2 - 2(4x - 3) (5x 2) (4x - 3)2` `

Question

Môn Toán Lớp 8:  Rút gọn bt `1,  (2x +1)^2 + (x -5)^2 - 5x (x -4)` `2, (3x+ 2)^2 - (3x - 1) (3x +1)` `3, (5x + 2)^2 - 2(4x - 3) (5x + 2) + (4x - 3)^2` `-` Mục đich để t check đáp án nká :'D.

tonhu12 · Answer

1)(2x+1)^2+(x-5)^2-5x(x-4)     ->  &Aacute;p dụng hằng đẳng thức:  (A+B)^2=A^2+2AB+B^2  v&agrave;  (A-B)^2=A^2-2AB+B^2     =>4x^2+4x+1+x^2-10x+25-5x^2+20x     =(4x^2+x^2-5x^2)+(4x-10x+20x)+(1+25)     =14x+26     2)(3x+2)^2-(3x-1)(3x+1)     =9x^2+12x+4+(-3x+1)(3x+1)     =9x^2+12x+4-9x^2-3x+3x+1     =(9x^2-9x^2)+(12x+3x-3x)+(1+4)     =12x+5     3)(5x+2)^2-2(4x-3)(5x+2)+(4x-3)^2     =25x^2+20x+4+(-8x+6)(5x+2)+16x^2-24x+9     =(25x^2+16x^2)+(20x-24x)+(4+9)-40x^2-16x+30x+12     =41x^2-4x+13-40x^2+14x+12     =(41x^2-40x^2)+(14x-4x)+(12+13)     =x^2+10x+25     =(x+5)^2

maianhnhiquynh · Answer

1) (2x+1)^2 + (x-5)^2 - 5x(x-4)   = 4x^2 + 4x + 1 + x^2 - 10x + 25 - 5x^2 +20x   = (4x^2 + x^2 -5x^2) + (4x - 10x + 20x) + 1 + 25   = 14x + 26   = 2(7x + 13)   2) (3x+2)^2 - (3x-1)(3x+1)   = 9x^2 + 12x + 4 - (9x^2 - 1)   = 9x^2 + 12x + 4 - 9x^2 + 1   = (9x^2 - 9x^2) + 12x + 4 + 1   = 12x + 5   3) (5x+2)^2 - 2(4x - 3)(5x+2) + (5x-3)^2   = 25x^2 + 20x + 4 - 2(20x^2+8x - 15x - 6) + 25x^2 - 30x + 9   = 25x^2 + 20x + 4 - 2(20x^2 - 7x - 6) + 25x^2 - 30x + 9   = 25x^2 + 20x + 4 - 40x^2 + 14x + 12 + 25x^2 - 30x + 9   = (25x^2 - 40x^2 +25x^2) + (20x + 14x - 30x) + (4+12+9)   = 10x^2 + 4x + 25

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Môn Toán Lớp 8: Rút gọn bt `1, (2x +1)^2 + (x -5)^2 – 5x (x -4)` `2, (3x+ 2)^2 – (3x – 1) (3x +1)` `3, (5x + 2)^2 – 2(4x – 3) (5x + 2) + (4x – 3)^2` `

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