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Cho a-3b=1, 2ab=-4. Tính:
A=2a+(7ab)/2-6b+2
B=(2a+6b)2-2
C= 3a2+27b2-ab-1
D= a3-27b3+a2+9b2+2
E=a4+81b4-1
\(3y^2\left(a-3x\right)-a\left(a-3x\right)=\left(3y^2-a\right)\left(a-3x\right)\)
a) a2 + b2 + 2ab + 2a + 2b + 1
= (a2 + b2 + 2ab) + (2a + 2b) + 1
= (a + b)2 + 2(a + b) + 1
= (a + b + 1)2
b) a3 - 3a + 3b - b3
= (a3 - b3) - (3a - 3b)
= (a - b)(a2 - ab + b2) - 3(a - b)
= (a - b)(a2 - ab + b2 - 3)
c) x2 + 2x - 15
= (x2 + 2x + 1) - 16
= (x + 1)2 - 16
= (x + 1 - 5)(x + 1 + 5)
= (x - 4)(x + 6)
d) a4 + 6a2b + 9b2 - 1
= (a2 + 3b)2 - 1
= (a2 + 3b - 1)(a2 + 3b + 1)
Lần sau tách từng câu nha, nhìn ngán quá!Câu nào dễ làm trước!
1.Sửa đề: \(A=27a^3-8=\left(3a\right)^3-2^3=\left(3a-2\right)\left[\left(3a\right)^2+2.\left(3a\right)+2^2\right]=\left(3a-2\right)\left(9a^2+6a+4\right)\)
3/ \(C=a^3-b^3+\left(a-b\right)^2=\left(a-b\right)\left(a^2+b^2+ab\right)+\left(a-b\right)^2=\left(a-b\right)\left(a^2+b^2+ab+a-b\right)\)
4/ \(D=\left(a^3+b^3\right)+\left(a+b\right)^2=\left(a+b\right)\left(a^2-ab+b^2\right)+\left(a+b\right)^2\)
\(=\left(a+b\right)\left(a^2-ab+b^2+a+b\right)\)
5 \(E=\left(a^2+1\right)^2-4a^2=\left(a^2+1\right)-\left(2a\right)^2\)
\(=\left(a^2-2a+1\right)\left(a^2+2a+1\right)\)
\(=\left[\left(a-1\right)\left(a+1\right)\right]^2=\left(a^2-1\right)^2\)
6/ \(F=\left(x^2+4\right)^2-16x^2=\left(x^2+4\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+4\right)\left(x^2+4x+4\right)\)
\(=\left[\left(x-2\right)\left(x+2\right)\right]^2=\left(x^2-4\right)^2\)
7) \(G=\left(a^2+2ab+b^2\right)-c^2=\left(a+b\right)^2-c^2=\left(a+b+c\right)\left(a+b-c\right)\)
8/\(I=1-\left(x^2-2xy+y^2\right)=1-\left(x-y\right)^2=\left(1-x+y\right)\left(1+x-y\right)\)
9/ \(U=2x^2+2y^2-4xy=2\left(x^2+y^2-2xy\right)=2\left(x-y\right)^2\)
2,
B = 8a3 - 27b3 - 2a(4a2 - 9b2)
= (2a - 3b)(4a2 + 6ab + 9b2) - 2a(2a - 3b)(2a + 3b)
= (2a - 3b) ( 4a2 + 6ab + 9b2 - 2a(2a + 3b))
= (2a - 3b) (4a2 + 6ab + 9b2 - 4a2 - 6ab)
= 9b2(2a - 3b)
Từ \(a^2-6b^2=-ab\Rightarrow a^2-6b^2+ab=0\)
\(\Rightarrow a^2+3ab-2ab-6b^2=0\)
\(\Rightarrow a\left(a+3b\right)-2b\left(a+3b\right)=0\)
\(\Rightarrow\left(a+3b\right)\left(a-2b\right)=0\)
\(\Rightarrow\orbr{\begin{cases}a+3b=0\\a-2b=0\end{cases}}\Rightarrow\orbr{\begin{cases}a=-3b\\a=2b\end{cases}}\)
- Xét \(a=-3b\) thay vào M ta có:
\(M=\frac{2\cdot3\left(-b\right)\cdot b}{2\left(-3b\right)^2-3b^2}=\frac{-6b^2}{15b^2}=-\frac{2}{5}\)
- Xét \(a=2b\) thay vào M ta có:
\(M=\frac{2\cdot2b\cdot b}{2\cdot\left(2b\right)^2-3b^2}=\frac{4b^2}{8b^2-3b^2}=\frac{4b^2}{5b^2}=\frac{4}{5}\)
\(\left(2a+b\right)^2-\left(2a+a\right)^2\)
\(=\left(2a+b-2a-a\right)\left(2a+b+2a+a\right)\)
\(=\left(b-a\right)\left(5a+b\right)\)
\(\left(2a+b\right)^2-\left(2a+a\right)^2\)
\(=\left(2a+b\right)^2-\left(3a\right)^2\)
\(=\left(2a+b-3a\right)\left(2a+b+3a\right)\)
\(=\left(b-a\right)\left(5a+b\right)\)