` 1)`
`a) 78^2 - 22^2`
`= ( 78 - 22 )(78+22)`
`= 56 . 100`
`= 5600`
`b) 97^2 - 3^2 `
`= ( 97-3)(97+3)`
`= 94 . 100`
`= 9400`
`c) 36^2 + 2.36.64 + 64^2`
`= ( 36 + 64)^2`
`= 100^2 `
`= 10000`
`d) 123^2 - 2.123.23 + 23^2`
`= ( 123 - 23 )^2`
`= 100^2`
`= 10000`
`e) 78^2 + 156.22 + 22^2`
`= 78^2 + 2.78.22 + 22^2`
`= ( 78+22)^2`
`= 100^2`
`= 10000`
`f) 149^2 - 149.98 + 49^2`
`= 149^2 - 149.2.49 + 49^2`
`= ( 149-49)^2`
`= 100^2`
`= 10000`
Bài `2 :`
`a) 9x^2 - 25 = ( 3x)^2 - 5^2 = (3x + 5)(3x - 5)`
`b) 64x^4 - 1 = ( 8x^2)^2 - 1^2 = (8x^2 - 1)(8x^2 + 1)`
`c) ( x + 2)^3 = x^3 + 6x^2 + 12x + 8`
`d) ( 3x + 2y )^3 = 27x^3 + 54x^2 y + 24xy^2 = 8y^3`
`f) ( 3x - 1)^3 = 27x^3 - 27x^2 + 9x - 1`
`g) ( x - y/3 )^3 = x^3 - x^2 y + \frac{xy^2}{3} - \frac{y^3}{27}`
`h) ( 2x - y/2 )^3 = 8x^3 - 6x^2 y + \frac{3xy^2}{2} - \frac{y^3}{8}`
Bài` 3 :`
`a) ( 4x - 1)^3 - ( 4x-3)(16x^2 + 3 )`
`= 64x^3 - 48x^2 + 12x - 1 - 64x^3 - 12x + 48x^2 + 9`
`= -1 + 9`
`= 8`
Vậy BT sau không phụ thuộc vào biến `x,y`
`=> ĐPCM`
`b) ( x + 1)^3 - ( x - 1)^3 - 6(x+1)(x-1)`
`= x^3 + 3x^2 + 3x + 1 - x^3 + 3x^2 - 3x + 1 - 6(x^2 - 1^2 )`
`= 6x^2 - 6x^2 + 2 - 6`
`= -4`
Vậy BT sau không phụ thuộc vào biến `x,y`
`=> ĐPCM`
Bài `4 :`
`a)` Đặt : `x^2 + 6x + 7` là `A`
`x^2 + 6x + 7 = ( x^2 + 6x + 9 ) - 2 = ( x + 3)^2 - 2`
Vì `( x + 3) ≥ 0 => ( x+3)^2 - 2 ≥ -2`
Dấu `"="` xảy ra khi :
`( x + 3)^2 = 0`
`<=> x + 3 = 0`
`<=> x = -3`
Vậy `Min(A) = -2 <=> x = -3`
`b)` Đặt : `9x^2 - 7x + 8` là `B`
`B = 9x^2 - 7x + 8`
`<=> ( 3x)^2 - 7x + 49/36 + 239/36`
`<=> ( 3x - 7/6 )^2 + 239/36`
Vì `(3x - 7/6 )^2 ≥ 0`
`=> ( 3x - 7/6 )^2 + 239/36 ≥ 239/36`
Dấu `"="` xảy ra khi :
`( 3x - 7/6 )^2 = 0`
`<=> 3x - 7/6 = 0`
`<=> x = 7/18`
Vậy `Min(B) = 239/36` khi `x = 7/18`
