Bài 1: Thu gọn biểu thức a) 6( 2x – 1 ) ² + 5( x – 2 )( x + 3 ) – 2( 5 – 2x ) ² b) ( 9x – 1 ) ² + ( 1 – 5x ) ² + 2( 9x – 1 )( 1 – 5x ) c) ( x ² – 5x

Bài 1: Thu gọn biểu thức
a) 6( 2x – 1 ) ² + 5( x – 2 )( x + 3 ) – 2( 5 – 2x ) ²
b) ( 9x – 1 ) ² + ( 1 – 5x ) ² + 2( 9x – 1 )( 1 – 5x )
c) ( x ² – 5x + 1 ) ² + 2( 5x – 1 )(x ² – 5x + 1 ) + ( 5x -1 ) ²
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  1. `a) 6(2x-1)^2 + 5(x-2)(x+3) – 2(5-2x)^2`

    `= 6(4x^2 – 4x + 1) + 5(x-2)(x+3) – 2(5-2x)^2`

    `= 6(4x^2-4x+1) + 5(x-2)(x+3) – 2(25-20x+4x^2)`

    `= 24x^2 – 24x + 6 + 5x^2 + 5x – 30 – 2(25-20x+4x^2)`

    `= 24x^2 – 24x + 6 + 5x^2 – 30 – 50 + 40x – 8x^2`

    `= 21x^2 + 21x – 74`

    `b) (9x-1)^2 + (1-5x)^2 + 2(9x-1)(1-5x)`

    `= 81x^2 – 18x + 1 + (1-5x)^2 + 2(9x-1)(1-5x)`

    `= 81x^2 – 18x + 1 + 1 – 10x + 25x^2 +2(9x-1)(1-5x)`

    `= 81x^2 – 18x + 1 + 1 – 10x + 25x^2 – 90x^2 + 28x – 2`

    `= 16x^2`

    `c) (x^2-5x+1)^2 + 2(5x-1)(x^2-5x+1)+(5x-1)^2`

    `= (x^2-5x+1)(x^2-5x+1) + 2(5x-1)(x^2-5x+1) + 25x^2 – 10x + 1`

    `= x^4 – 10x^3 + 27x^2 – 10x + 1 + 2(5x-1)(x^2-5x+1)+25x^2 – 10x + 1`

    `= x^4 – 10x^3 + 27x^2 – 10x + 1 + 10x^3 – 52x^2 + 20x – 2 + 25x^2 – 10x + 1`

    `= x^4`

     

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  2. `a)6(2x-1)²+5(x-2)(x+3)-2(5-2x)²`

    `=6(4x²-4x+1)+(5x-10)(x+3)-2(25-20x+4x²)`

    `=24x²-24x+6+5x²+15x-10x-30-50+40x-8x²`

    `=(24x²+5x²-8x²)+(-24x+15x-10x+40x)+(6-30-50)`

    `=21x²+21x-74`

    `b)(9x-1)²+(1-5x)²+2(9x-1)(1-5x)`

    `=81x²-18x+1+1-10x+25x²+(18x-2)(1-5x)`

    `=81x²-18x+1+1-10x+25x²+18x-90x²-2+10x`

    `=(81x²+25x²-90x²)+(-18x-10x+18x+10x)+(1+1-2)`

    `=16x²`

    `c)(x²-5x+1)²+2(5x-1)(x²-5x+1)+(5x-1)²`

    `=(x²-5x+1+5x-1)²`

    `=(x²)²`

    `=x^4`

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