Rút gọn các biểu thức sau:
a) xy(x^5 − y^3) − x^2.y(x^4 − y^3)
b) x^3.y^4.(x^2 − y^3) − x^3.y^3(x^4-y^4)
Rút gọn rồi tính
a) A = x^3(x^2 − y^3) − y^3(y^2 − x^3) với x = 2; y = −2;
b) B = (−x^2.y)(x^2.y^2 − 2x) + x.y^3(x^3 − x.y^3) với x = 3; y = 2.
Tính A = x5 − 70×4 − 70×3 − 70×2 − 70x + 29 bằng cách hợp lí tại x = 71.
Đáp án:
1) a) `=x^2y^4−xy^4`
b) `=x^5y^4−x^7y^3`
2)
a) `-32`
b) `-468`
c) `100`
Giải thích các bước giải:
1)
a) `xy(x^5−y^3)−x^2xxy(x^4−y^3)`
`=x^6y−xy^4−x^6y+x^2y^4`
`=x^2y^4−xy^4.`
b) `x^3y^4xx(x^2−y^3)−x^3y^3xx(x^4−y^4)`
`=x^5y^4−x^3y^7−x^7y^3+x^3y^7`
`=x^5y^4−x^7y^3.`
2)
a) `A=x^3(x^2−y^3)−y^3(y^3−x^3)`
`=x^5−x^3y^3−y^6+x^3y^3`
`=x^5−y^6`
`=2^5−(−2)^6`
`=32−64`
`=−32.`
b) `B=(−x^2y)(x^2y^2−2x)+xy^3(x^3−xy^3)`
`=−x^4y^3+2x^3y+x^4y^3−x^2y^6`3)`
`=−x^4y^3+2x^3y+x^4y^3−x^2y^6`
`=2x^3y−x^2y^6`
`=2xx3^3xx2−3^2xx2^6`
`=108−576`
`=−468.`
c) ` A=x^5−70x^4−70x^3−70x^2−70x+29`
`=x^5−(x−1)x^4−(x−1)x^3−(x−1)x^2−(x−1)x+29`
`=x^5−x^5+x^4−x^4+x^3−x^3+x^2−x^2+x+29`
`=x+29`
`71+29`
`=100.`
1/
a/ $xy(x^5-y^3)-x^2.y(x^4-y^3)$
$=x^6y-xy^4-x^6y+x^2y^4$
$=x^2y^4-xy^4$
b/ $x^3y^4.(x^2-y^3)-x^3y^3.(x^4-y^4)$
$=x^5y^4-x^3y^7-x^7y^3+x^3y^7$
$=x^5y^4-x^7y^3$
2/
a/ $A=x^3(x^2-y^3)-y^3(y^3-x^3)$
$=x^5-x^3y^3-y^6+x^3y^3$
$=x^5-y^6$
$=2^5-(-2)^6$
$=32-64$
$=-32$
b/ $B=(-x^2y)(x^2y^2-2x)+xy^3(x^3-xy^3)$
$=-x^4y^3+2x^3y+x^4y^3-x^2y^6$
$=2x^3y-x^2y^6$
$=2.3^3.2-3^2.2^6$
$=108-576$
$=-468$
c/ $A=x^5-70x^4-70x^3-70x^2-70x+29$
$=x^5-(x-1)x^4-(x-1)x^3-(x-1)x^2-(x-1)x+29$
$=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+29$
$=x+29$
$=71+29$
$=100$
Chúc bạn học tốt !!!