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c)\(x^2+x+\dfrac{1}{4}=\left(x+\dfrac{1}{2}\right)^2\)
d)\(\dfrac{a^2}{4}-2a+4=\left(\dfrac{a}{2}-2\right)^2\)
e) \(4y^2-9x^2=\left(2y-3x\right)\left(2y+3x\right)\)
f)\(9y^2-\dfrac{1}{4}=\left(3y-\dfrac{1}{2}\right)\left(3y+\dfrac{1}{2}\right)\)
g)\(8x^3+8a^3=\left(2x+2a\right)\left(4x^2-4xa+4a^2\right)\)
a)\(\left(a^3-b^3\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)
\(\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)
b) \(\left(8a^3-27b^3\right)-2a\left(4a^2-9b^2\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2\right)-2a\left(2a-3b\right)\left(2a+3b\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2-4a^2-6ab\right)\)
\(=\left(2a-3b\right)\cdot9b^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+a^2-2ab+b^2\)
= ...........
\(3y^2\left(a-3x\right)-a\left(a-3x\right)=\left(3y^2-a\right)\left(a-3x\right)\)
\(\left(2a+b\right)^2-\left(2a+a\right)^2\)
\(=\left(2a+b-2a-a\right)\left(2a+b+2a+a\right)\)
\(=\left(b-a\right)\left(5a+b\right)\)
\(\left(2a+b\right)^2-\left(2a+a\right)^2\)
\(=\left(2a+b\right)^2-\left(3a\right)^2\)
\(=\left(2a+b-3a\right)\left(2a+b+3a\right)\)
\(=\left(b-a\right)\left(5a+b\right)\)
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)
Hãy điền biểu thức thích hợp vào chỗ trống(...)
a) (1/2-a)3=1/8-3/4a+...-a3
b)(ax+13)=...+3a2x4+3ax2+1
a) (4a-3b) (16a2 + 12ab + 9b2 ) = 64a3 - 27b3
b) (2a+b) ( 4a2 - 2ab + b2) = 8a3 + b3