Đáp án + Giải thích các bước giải:
`a) 1/4a^2-b^2=(1/2a+b)(1/2a-b)`
`b) 49-a^4b^2=(7-a^2b)(7+a^2b)`
`c) a^2x^2-1/4b^2=(ax-1/2b)(ax+1/2b)`
`d) a^4-b^4=(a^2-b^2)(a^2+b^2)`
`e) 4p^2-9=(2p-3)(2p+3)`
`f) c^2d^4`
`g) 81a^2b^2-x^2=(9ab-x)(9ab+x)`
`h) (5a+3b)^2-25=(5a+3b-5)(5a+3b+5)`
`i) (a+3y)^2-z^2=(a+3y-z)(a+3y+z)`
`k) a^2b-b^3(x+y)^2= b[a^2-b^2(x+y)^2]`
`=b[a-b(x+y)][a+b(x+y)]`
`=b(a-bx-by)(a+bx+by)`
`m) (xy)^2-(x-y)^2`
`=(xy-x+y)(xy+x-y)`
`n) 1-(x-y)^2=(1-x+y)(1+x-y)`
`l) 16a^2-(x-y)^2=(4a-x+y)(4a+x-y)`
`p) (a-3b)^2-16c^2=(a-3b-4c)(a-3b+4c)`
`q) 9a^2+6ab+b^2=93x+b)^2`
`u) 1-a^3=(1-a)(1+a+a^2)`
`v) 64x^3+1/8=(4x+1/2)(16x^2-2x+1/4)`
`w) a^3-27=(a-3)(a^2+3a+9)`
`y) x^3-3x^2+3x-1=(x-1)^3`
Áp dụng: `a^2-b^2=(a-b)(a+b)`
`a^3-b^3=(a-b)(a^2+ab+b^2)`
`a^3+b^3=(a+b)(a^2-2ab+b^2)`