đưa các biểu thức sau về dạng bình phương 1 hiệu:
4a^2-4a+1
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a) \(x^2-6x-y^2-4y+5=x^2-6x+9-y^2-4y-4\)
\(=\left(x^2-6x+9\right)-\left(y^2+4y+4\right)=\left(x-3\right)^2-\left(y+2\right)^2\)
b) \(4a^2-12a-b^2+2b+8=4a^2-12a+9-b^2+2b-1\)
\(=\left(4a^2-12a+9\right)-\left(b^2-2b+1\right)=\left(2a-3\right)^2-\left(b-1\right)^2\)
x2 - 6x - y2 - 4y + 5
= ( x2 - 6x + 9 ) - ( y2 + 4y + 4 )
= ( x - 3 )2 - ( y + 2 )2
4a2 - 12a - b2 + 2b + 8
= ( 4a2 - 12a + 9 ) - ( b2 - 2b + 1 )
= ( 2a - 3 )2 - ( b - 1 )2
1) \(\left(3x-2\right)^2=9x^2-12x+4\)
\(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2=\dfrac{1}{4}x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\)
\(\left(a+b\sqrt{3}\right)^2=a^2+2\sqrt{3}ab+3b^2\)
2) \(4a^2+4a+1=\left(2a+1\right)^2\)
\(9x^2-6x+1=\left(3x-1\right)^2\)
\(\dfrac{1}{4}x^2-\dfrac{1}{3}xy+\dfrac{1}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{1}{3}y\right)^2\)
67x73 = (70-3)(70+3) = 702 - 32 = 4900 - 9 = 4801.
a) \(16a^2-24ab+9b^2=\left(4a-3b\right)^2.\)
b) \(a^2+4ab+4b^2=\left(a+2b\right)^2\)
TL:
67 x 73 = ( 70 - 3 ) ( 70 + 3 ) = 702 - 32 = 4900 - 9 = 4801
a) \(16a^2\)\(-24ab+9ab=\left(4a-3b\right)^2\)
b) \(a^2\)\(+4ab+4b^2\)\(=\left(a+2b\right)^2\)
~HT~
a) \(x^4+4x^2+4=\left(x^2+2\right)^2\)
b) \(\left(2y-x\right)^2+2\left(2y-x\right)+1=\left(2y-x+1\right)^2\)
c) \(\left(2a-4b\right)^2+4a-8b+1=\left(2a-4b\right)^2+2\cdot\left(2a-4b\right)\cdot1+1^2=\left(2a-4b+1\right)^2\)
\(4a^2-4a+1\)
\(=\left(2a\right)^2-2.2a.1+1^2\)
\(=\left(2a-1\right)^2\)
ms lên lớp 8 à hk tốt nha