Hướng dẫn trả lời:
Bài 17:
Áp dụng HĐT số 3 `a^2 - b^2 = (a + b).(a - b).`
1) `3^2 - x^2 = (3 + x).(3 - x).`
2) `x^2 - 36 = x^2 - 6^2 = (x + 6).(x - 6).`
3) `y^2 - 1 = y^2 - 1^2 = (y + 1).(y - 1).`
4) `25 - y^2 = 5^2 - y^2 = (5 + y).(5 - y).`
5) `9x^2 - 1 = (3x)^2 - 1^2 = (3x + 1).(3x - 1).`
6) `1/25 - 4x^2 = (1/5)^2 - (2x)^2 = (1/5 + 2x).(1/5 - 2x).`
7) `9x^2 - y^2 = (3x)^2 - y^2 = (3x + y).(3x - y).`
8) `x^2 - 4y^2 = x^2 - (2y)^2 = (x + 2y).(x - 2y).`
Bài 18:
Áp dụng HĐT số 3 `a^2 - b^2 = (a + b).(a - b).`
1) `(x - 5).(x + 5)`
`= x^2 - 5^2`
`= x^2 - 25.`
2) `(4 - x).(4 + x)`
`= 4^2 - x^2`
`= 16 - x^2.`
3) `(x - 2/3).(x + 2/3)`
`= x^2 - (2/3)^2`
`= x^2 - 4/9.`
4) `(1 + 2x).(1 - 2x)`
`= 1^2 - (2x)^2`
`= 1 - 4x^2.`
5) `- (2x + 3).(3 - 2x)`
`= - (2x + 3). - (2x - 3)`
`= (2x + 3).(2x - 3)`
`= (2x)^2 - 3^2 = 4x^2 - 9.`
6) Cách 1: `-(5x - 3).(3 + 5x)`
`= -(5x - 3).(5x + 3)`
`= - [(5x)^2 - 3^2]`
`= - (25x^2 - 9).`
`= - 25x^2 + 9.`
Cách 2: `-(5x - 3).(3 + 5x)`
`= -[-(3 - 5x).(3 + 5x)]`
`= (3 - 5x).(3 + 5x)`
`= 3^2 - (5x)^2.`
`= 9 - 25x^2.`
7) `- (3x - 2/5).(3x + 2/5)`
`= - [(3x)^2 - (2/5)^2]`
`= - (9x^2 - 4/25)`
`= - 9x^2 + 4/25.`
8) `-(2x - 2/3).(2x + 2/3)`
`= -[(2x)^2 - (2/3)^2]`
`= - (4x^2 - 4/9)`
`= - 4x^2 + 4/9.`
