Question

Thu gọn, chỉ ra phần hệ số và tìm bậc của các đơn thức sau:

1) A= \(\frac34\) \(x^{n-1}\) . \(\frac45x^{2n+1}\) \(y^{2n+1}\) . \(\frac56xy^{n+1}\)

2) B= \(\frac64x^{3-n}\) .\(\frac42x^{4-n}\) \(y^{5-n}\) .\(\frac26y^{6-n}\)

3) C= \(\frac{-4}{3}x^{2-n}\) \(y\) .\(\frac67x^{2n-3}\) \(y^{n-1}\) .\(\frac{-1}{2}xy\)

4) D=\(\frac15xy^{n+1}\) .\(\frac43x^{n+1}y\) . \(\frac{15}{7}x^{n}y^{n}\)

Answer 1

Đơn thức AThu gọn: A = (1/2) * x^(3n + 1) * y^(3n + 2)Hệ số: 1/2Bậc: 6n + 3Đơn thức BThu gọn: B = x^(7 - 2n) * y^(11 - 2n)Hệ số: 1Bậc: 18 - 4nĐơn thức CThu gọn: C = (4/7) * x^n * y^(n + 2)Hệ số: 4/7Bậc: 2n + 2Đơn thức DThu gọn: D = (4/7) * x^(2n + 2) * y^(2n + 2)Hệ số: 4/7Bậc: 4n + 4

Answer 2

1) A=\(\left(\frac34\cdot\frac45\cdot\frac56\right)\cdot\left(x^{n-1}\cdot x^{2n+1}\cdot x\right)\left(y^{2n+1}\cdot y^{n+1}\right)\)

\(A=\frac12\cdot x^{n-1+2n+1+1}\cdot y^{2n+1+n+1}\)

\(A=\frac12x^{3n+1}y^{3n+2}\)

hệ số : \(\frac12\)

bậc của đơn thức: (3n+1)+(3n+2)=6n+3

2) \(B=\left(\frac64\cdot\frac42\cdot\frac26\right)\cdot\left(x^{3-n}\cdot x^{4-n}\right)\left(y^{5-n}\cdot y^{6-n}\right)\)

\(B=1\cdot x^{3-n+4-n}\cdot y^{5-n+6-n}\)

\(B=x^{7-2n}\cdot y^{11-2n}\)

hệ số: 1

bậc của đơn thức: (7-2n)+(11-2n)=18-4n

3) \(C=\left(\frac{-4}{3}\cdot\frac67\cdot\frac{-1}{2}\right)\cdot\left(x^{2-n}\cdot x^{2n-3}\cdot x\right)\left(y\cdot y^{n-1}\cdot y\right)\)

\(C=\frac47\cdot x^{2-n+2n-3+1}\cdot y^{1+n-1+1}\)

\(C=\frac47x^{n}\cdot y^{n+1}\)

hệ số: \(\frac47\)

bậc của đơn thức: n+(n+1)=2n+1

4) \(D=\left(\frac15\cdot\frac43\cdot\frac{15}{7}\right)\cdot\left(x\cdot x^{n+1}\cdot x^{n}\right)\left(y^{n+1}\cdot y\cdot y^{n}\right)\)

\(C=\frac47\cdot x^{1+n+1+n}\cdot y^{n+1+1+n}\)

\(C=\frac47x^{2n+2}\cdot y^{2n+2}\)

hệ số: \(\frac47\)

bậc của đơn thức: (2n+2)+(2n+2)=4n+4

Answer 3

1) Đơn thức \(A\)\(A = \frac{3}{4} x^{n-1} \cdot \frac{4}{5} x^{2n+1} y^{2n+1} \cdot \frac{5}{6} x y^{n+1}\)Thu gọn:
\(A = \left( \frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \right) \cdot \left( x^{n-1} \cdot x^{2n+1} \cdot x^1 \right) \cdot \left( y^{2n+1} \cdot y^{n+1} \right)\)
\(A = \frac{1}{2} x^{(n-1) + (2n+1) + 1} y^{(2n+1) + (n+1)}\)
\(A = \frac{1}{2} x^{3n+1} y^{3n+2}\)Hệ số: \(\frac{1}{2}\)Bậc: \((3n+1) + (3n+2) = 6n+3\)2) Đơn thức \(B\)\(B = \frac{6}{4} x^{3-n} \cdot \frac{4}{2} x^{4-n} y^{5-n} \cdot \frac{2}{6} y^{6-n}\)Thu gọn:
\(B = \left( \frac{6}{4} \cdot \frac{4}{2} \cdot \frac{2}{6} \right) \cdot \left( x^{3-n} \cdot x^{4-n} \right) \cdot \left( y^{5-n} \cdot y^{6-n} \right)\)
\(B = 1 \cdot x^{(3-n) + (4-n)} y^{(5-n) + (6-n)}\)
\(B = x^{7-2n} y^{11-2n}\)Hệ số: \(1\)Bậc: \((7-2n) + (11-2n) = 18-4n\)3) Đơn thức \(C\)\(C = \frac{-4}{3} x^{2-n} y \cdot \frac{6}{7} x^{2n-3} y^{n-1} \cdot \frac{-1}{2} xy\)Thu gọn:
\(C = \left( \frac{-4}{3} \cdot \frac{6}{7} \cdot \frac{-1}{2} \right) \cdot \left( x^{2-n} \cdot x^{2n-3} \cdot x^1 \right) \cdot \left( y^1 \cdot y^{n-1} \cdot y^1 \right)\)
\(C = \frac{4}{7} x^{(2-n) + (2n-3) + 1} y^{1 + (n-1) + 1}\)
\(C = \frac{4}{7} x^n y^{n+1}\)Hệ số: \(\frac{4}{7}\)Bậc: \(n + (n+1) = 2n+1\)4) Đơn thức \(D\)\(D = \frac{1}{5} x y^{n+1} \cdot \frac{4}{3} x^{n+1} y \cdot \frac{15}{7} x^n y^n\)Thu gọn:
\(D = \left( \frac{1}{5} \cdot \frac{4}{3} \cdot \frac{15}{7} \right) \cdot \left( x^1 \cdot x^{n+1} \cdot x^n \right) \cdot \left( y^{n+1} \cdot y^1 \cdot y^n \right)\)
\(D = \frac{4}{7} x^{1 + (n+1) + n} y^{(n+1) + 1 + n}\)
\(D = \frac{4}{7} x^{2n+2} y^{2n+2}\)Hệ số: \(\frac{4}{7}\)Bậc: \((2n+2) + (2n+2) = 4n+4\)oh xin tích

Answer 4

1) Đơn thức \(A\)\(A = \frac{3}{4}x^{n-1} \cdot \frac{4}{5}x^{2n+1}y^{2n+1} \cdot \frac{5}{6}xy^{n+1}\)Thu gọn:
\(A = \left( \frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \right) \cdot (x^{n-1} \cdot x^{2n+1} \cdot x) \cdot (y^{2n+1} \cdot y^{n+1})\)
\(A = \frac{1}{2}x^{(n-1) + (2n+1) + 1} \cdot y^{(2n+1) + (n+1)}\)
\(A = \frac{1}{2}x^{3n+1}y^{3n+2}\)Hệ số: \(\frac{1}{2}\)Bậc: \((3n+1) + (3n+2) = \mathbf{6n+3}\)2) Đơn thức \(B\)\(B = \frac{6}{4}x^{3-n} \cdot \frac{4}{2}x^{4-n}y^{5-n} \cdot \frac{2}{6}y^{6-n}\)Thu gọn:
\(B = \left( \frac{6}{4} \cdot \frac{4}{2} \cdot \frac{2}{6} \right) \cdot (x^{3-n} \cdot x^{4-n}) \cdot (y^{5-n} \cdot y^{6-n})\)
\(B = 1 \cdot x^{(3-n) + (4-n)} \cdot y^{(5-n) + (6-n)}\)
\(B = x^{7-2n}y^{11-2n}\)Hệ số: \(1\)Bậc: \((7-2n) + (11-2n) = \mathbf{18-4n}\)3) Đơn thức \(C\)\(C = \frac{-4}{3}x^{2-n}y \cdot \frac{6}{7}x^{2n-3}y^{n-1} \cdot \frac{-1}{2}xy\)Thu gọn:
\(C = \left( \frac{-4}{3} \cdot \frac{6}{7} \cdot \frac{-1}{2} \right) \cdot (x^{2-n} \cdot x^{2n-3} \cdot x) \cdot (y \cdot y^{n-1} \cdot y)\)
\(C = \frac{4}{7}x^{(2-n) + (2n-3) + 1} \cdot y^{1 + (n-1) + 1}\)
\(C = \frac{4}{7}x^n y^{n+1}\)Hệ số: \(\frac{4}{7}\)Bậc: \(n + (n+1) = \mathbf{2n+1}\)4) Đơn thức \(D\)\(D = \frac{1}{5}xy^{n+1} \cdot \frac{4}{3}x^{n+1}y \cdot \frac{15}{7}x^n y^n\)Thu gọn:
\(D = \left( \frac{1}{5} \cdot \frac{4}{3} \cdot \frac{15}{7} \right) \cdot (x \cdot x^{n+1} \cdot x^n) \cdot (y^{n+1} \cdot y \cdot y^n)\)
\(D = \frac{4}{7}x^{1 + (n+1) + n} \cdot y^{(n+1) + 1 + n}\)
\(D = \frac{4}{7}x^{2n+2}y^{2n+2}\)Hệ số: \(\frac{4}{7}\)Bậc: \((2n+2) + (2n+2) = \mathbf{4n+4}\)

Answer 5

A = (3/4).(4/5).(5/6)x^(n-1+2n+1+1)y^(2n+1+n+1)
= 1/2 x^(3n+1)y^(3n+2)

Hệ số là 1/2

Bậc là (3n + 1) + (3n + 2) = 6n + 3

B = (6/4).(4/2).(2/6)x^(3-n+4-n)y^(5-n+6-n)
= x^(7-2n)y^(11-2n)

Hệ số là 1

Bậc là (7 - 2n) + (11 - 2n) = 18 - 4n

C = (-4/3).(6/7).(-1/2)x^(2-n+2n-3+1)y^(1+n-1+1)
= 4/7 x^n y^(n+1)

Hệ số là 4/7

Bậc là n + (n + 1) = 2n + 1

D = (1/5).(4/3).(15/7)x^(1+n+1+n)y^(n+1+1+n)
= 4/7 x^(2n+2)y^(2n+2)

Hệ số là 4/7

Bậc là (2n + 2) + (2n + 2) = 4n + 4