Phan tich da thic thanh nhan tu
a)A=ab^3c^2-a^2b^2c^2+ab^2c^3-a^2bc^3
b)B=7-12x-4x^2
c)C=4x^2-15x+14
d)D= 5x^2-30xy+25y^2
Phan tich da thic thanh nhan tu
a)A=ab^3c^2-a^2b^2c^2+ab^2c^3-a^2bc^3
b)B=7-12x-4x^2
c)C=4x^2-15x+14
d)D= 5x^2-30xy+25y^2
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
A = a{b^3}{c^2} – {a^2}{b^2}{c^2} + a{b^2}{c^3} – {a^2}b{c^3}\\
= \left( {a{b^3}{c^2} – {a^2}{b^2}{c^2}} \right) + \left( {a{b^2}{c^3} – {a^2}b{c^3}} \right)\\
= a{b^2}{c^2}\left( {b – a} \right) + ab{c^3}\left( {b – a} \right)\\
= \left( {b – a} \right)\left( {a{b^2}{c^2} + ab{c^3}} \right)\\
= \left( {b – a} \right).ab{c^2}.\left( {b + c} \right)\\
= ab{c^2}\left( {b – a} \right)\left( {b + c} \right)\\
b,\\
B = 7 – 12x – 4{x^2}\\
= \left( { – 4{x^2} + 2x} \right) – \left( {14x – 7} \right)\\
= – 2x\left( {2x – 1} \right) – 7\left( {2x – 1} \right)\\
= – \left( {2x – 1} \right)\left( {2x + 7} \right)\\
c,\\
C = 4{x^2} – 15x + 14\\
= \left( {4{x^2} – 8x} \right) – \left( {7x – 14} \right)\\
= 4x\left( {x – 2} \right) – 7\left( {x – 2} \right)\\
= \left( {x – 2} \right)\left( {4x – 7} \right)\\
d,\\
D = 5{x^2} – 30xy + 25{y^2}\\
= 5\left( {{x^2} – 6xy + 5{y^2}} \right)\\
= 5.\left[ {\left( {{x^2} – xy} \right) – \left( {5xy – 5{y^2}} \right)} \right]\\
= 5.\left[ {x\left( {x – y} \right) – 5y\left( {x – y} \right)} \right]\\
= 5.\left( {x – y} \right)\left( {x – 5y} \right)
\end{array}\)