Đáp án:
Bài 1 :
`a, (2x+1)^2 - (x-1)^2`
`= (2x+1-x+1)(2x+1+x-1)`
`= 3x(x+2)`
`b, 9(x+5)^2-(x-7)^2`
`= [3(x+5)]^2-(x-7)^2`
`= [3(x+5)-(x-7)][3(x+5)+(x-7)]`
`= (3x+15-x+7)(3x+15+x-7)`
`= (2x+22)(4x+8)`
`= 2(x+11). 4(x+2)`
`= 8(x+11)(x+2)`
`c, 25(x-y)^2-16(x+y)^2`
`= [5(x-y)]^2-[4(x+y)]^2`
`= [5(x-y)-4(x+y)][5(x-y)+4(x+y)]`
`= (5x-5y-4x-4y)(5x-5y+4x+4y)`
`= (x-9y)(9x-y)
`d, 49(y-4)^2-9(y+2)^2`
`= [7(y-4)]^2-[3(y+2)]^2`
`= [7(y-4)-3(y+2)][7(y-4)+3(y+2)]`
`= (7y-28-3y-6)(7y-28+3y+6)`
`= (4y-34)(10y-22)`
`= 2(2y-17). 2(5y-11)`
`= 4(2y-17)(5y-11)`
Bài 2:
`a, x^4+x^3+x+1`
`= (x^4+x^3)+(x+1)`
`= x^3(x+1)+(x+1)`
`= (x+1)(x^3+1)`
`= (x+1)(x+1)(x^2-x+1)`
`= (x+1)^2 (x^2-x+1)`
`b, x^4-x^3-x+1`
`= (x^4-x^3)-(x-1)`
`= x^3(x-1)-(x-1)`
`= (x-1)(x^3-1)`
`= (x-1)(x-1)(x^2+x+1)`
`= (x-1)^2 (x^2-x+1)`
`c, x^2y+xy^2-x-y`
`= (x^2y+xy^2)-(x+y)`
`= xy(x+y)-(x+y)`
`= (x+y)(xy-1)`
`d, a^2x+a^2y-7x-7y`
`= (a^2x+a^2y)-(7x+7y)`
`= a^2(x+y)-7(x+y)`
`= (x+y)(a^2-7)`
`e, ax^2+ay-bx^2-by`
`= (ax^2+ay)-(bx^2+by)`
`= a(x^2+y)-b(x^2+y)`
`= (x^2+y)(a-b)`
`f, x(x+1)^2+x(x-5)-5(x+1)^2`
`= [x(x+1)^2-5(x+1)^2]+x(x-5)`
`= (x+1)^2(x-5)+x(x-5)`
`= (x-5)[(x+1)^2+x]`
`= (x-5)(x^2+2x+1+x)`
`= (x-5)(x^2+3x+1)`
