Toán Lớp 8: Phân tích đa thức thành nhân tử:
a) 43^2 − 11^2/(36,5)^2-(27,5)^2; b) 97^3-83^3/180-97.83
c) A= x(2x –y) –z(y -2x) với x =1,2 ; y= 1,4 ; z=1,8 ;
d) B=(x -1)x2 – 4x (x- 1) + 4( x- 1) với x =3
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Toán Lớp 8: Phân tích đa thức thành nhân tử:
a) 43^2 − 11^2/(36,5)^2-(27,5)^2; b) 97^3-83^3/180-97.83
c) A= x(2x –y) –z(y -2x) với x =1,2 ; y= 1,4 ; z=1,8 ;
d) B=(x -1)x2 – 4x (x- 1) + 4( x- 1) với x =3
Comments ( 1 )
a)\dfrac{{{{43}^2} – {{11}^2}}}{{36,{5^2} – 27,{5^2}}}\\
= \dfrac{{\left( {43 + 11} \right)\left( {43 – 11} \right)}}{{\left( {36,5 – 27,5} \right)\left( {36,5 + 27,5} \right)}}\\
= \dfrac{{54.32}}{{9.64}}\\
= 3\\
b)\dfrac{{{{97}^3} + {{83}^3}}}{{180}} – 97.83\\
= \dfrac{{\left( {97 + 83} \right)\left( {{{97}^2} – 97.83 + {{83}^2}} \right)}}{{180}} – 97.83\\
= {97^2} – 97.83 + {83^2} – 97.83\\
= {\left( {97 – 83} \right)^2}\\
= {14^2}\\
= 196\\
c)A = x\left( {2x – y} \right) – z\left( {y – 2x} \right)\\
= \left( {2x – y} \right).\left( {x + z} \right)\\
= \left( {2.1,2 – 1,4} \right).\left( {1,2 + 1,8} \right)\\
= 1.3\\
= 3\\
d)B = \left( {x – 1} \right){x^2} – 4x\left( {x – 1} \right) + 4\left( {x – 1} \right)\\
= \left( {x – 1} \right)\left( {{x^2} – 4x + 4} \right)\\
= \left( {x – 1} \right){\left( {x – 2} \right)^2}\\
= \left( {3 – 1} \right){\left( {3 – 2} \right)^2}\\
= 2.1\\
= 2
\end{array}$