Giúp mik với ạ
Phân tích các đa thức sau thành nhân tử:
1)4a^2b^4 – c^4d^2
2)100x^2 – (3x-y)^2
3)(a+b)^2 – (2a-b)^2
4)(3x+1)^2 – 4(x-2)^2
Giúp mik với ạ Phân tích các đa thức sau thành nhân tử: 1)4a^2b^4 – c^4d^2 2)100x^2 – (3x-y)^2 3)(a+b)^2 – (2a-b)^2 4)(3x+1)^2 – 4(x-2)^2
By Emery
$$\eqalign{
& 1)\,\,4{a^2}{b^4} – {c^4}{d^2} \cr
& = {\left( {2a{b^2}} \right)^2} – {\left( {{c^2}d} \right)^2} \cr
& = \left( {2a{b^2} – {c^2}d} \right)\left( {2a{b^2} + {c^2}d} \right) \cr
& 2)\,\,100{x^2} – {\left( {3x – y} \right)^2} \cr
& = {\left( {10x} \right)^2} – {\left( {3x – y} \right)^2} \cr
& = \left( {10x – 3x + y} \right)\left( {10x + 3x – y} \right) \cr
& = \left( {7x + y} \right)\left( {13x – y} \right) \cr
& 3)\,\,{\left( {a + b} \right)^2} – {\left( {2a – b} \right)^2} \cr
& = \left( {a + b – 2a + b} \right)\left( {a + b + 2a – b} \right) \cr
& = 3a\left( {2b – a} \right) \cr
& 4)\,\,{\left( {3x + 1} \right)^2} – 4{\left( {x – 2} \right)^2} \cr
& = {\left( {3x + 1} \right)^2} – {\left[ {2\left( {x – 2} \right)} \right]^2} \cr
& = {\left( {3x + 1} \right)^2} – {\left( {2x – 4} \right)^2} \cr
& = \left( {3x + 1 – 2x + 4} \right)\left( {3x + 1 + 2x – 4} \right) \cr
& = \left( {x + 5} \right)\left( {5x – 3} \right) \cr} $$