giải gấp giúp mình ạ.
`#\text{nn}`
`1,`
`1)`
\(\left(3x-1\right)^2\\ =\left(3x\right)^2-2\cdot3x\cdot1+1^2\\ =9x^2-6x+1\)
`2)`
\(\left(2y+3x\right)^2\\ =\left(2y\right)^2+2\cdot2y\cdot3x+\left(3x\right)^2\\ =4y^2+12xy+9x^2\)
`3)`
\(\left(4x-5\right)^2\\ =16x^2-40x+25\)
`4)`
\(4y^2-9\\ =\left(2y\right)^2-3^2\\ =\left(2y-3\right)\left(2y+3\right)\)
`5)`
\(64x^2-25y^2\\ =\left(8x^2\right)-\left(5y\right)^2\\ =\left(8x-5y\right)\left(8x+5y\right)\)
`6)`
\(\left(2x^3-1\right)^2\\ =\left(2x^3\right)^2-2\cdot2x^3\cdot1+1^2\\ =8x^6-4x^3+1\)
`7)`
\(\left(5xy+7\right)^2\\ =\left(5xy\right)^2+2\cdot5xy\cdot7+7^2\\ =25x^2y^2+70xy+49\)
`8)`
\(\left(3x+8ay^2\right)^2\\ =\left(3x\right)^2+2\cdot3x\cdot8ay^2+\left(8ay^2\right)^2\\ =9x^2+48xay^2+64a^2y^4\)
`9)`
\(\left(a+b\right)^2-\left(a-b\right)^2\\ =\left(a+b-a+b\right)\left(a+b+a-b\right)\\ =2b\cdot2a\\ =4ab\)
`10)`
\(84^2-16^2\\ =\left(84-16\right)\left(84+16\right)\\ =68\cdot100\\ =6800\)
`11)`
\(\left(3xy-z\right)\left(3xy+z\right)\\ =\left(3xy\right)^2-z^2\\ =9x^2y^2-z^2\)
`12)`
\(\left(x^2+5\right)\left(5-x^2\right)\\ =\left(5+x^2\right)\left(5-x^2\right)\\ =5^2-\left(x^2\right)^2\\ =25-x^4\)
`2,`
`1)`
`4x^2 - 12x + 9`
`= (2x)^2 - 2*2x*3 + 3^2`
`= (2x - 3)^2`
`2)`
`36x^2 + 24xy + 4y^2`
`= (6x)^2 + 2*6x*2y (2y)^2`
`= (6x + 2y)^2`
`3)`
`9x^2y^2 - 2xy^2 + 1/9y^2`
`= (3xy)^2 - 2*3xy*1/3y + (1/3y)^2`
`= (3xy - 1/3y)^2`
`4)`
`25x^4 + 10x^2y^3 + y^6`
`= (5x^2)^2 + 2*5x^2*y^3 + (y^3)^2`
`= (5x^2 + y^3)^2`
___
2 HĐT được sử dụng:
`@` `(A + B)^2 = A^2 + 2AB + B^2`
`@` `(A - B)^2 = A^2 - 2AB + B^2`
`3,`
`a,`
`(x^2 + y^2)^2 - 4x^2y^2`
`= (x^2)^2 + 2*x^2*y^2 + (y^2)^2 - 4x^2y^2`
`= x^4 + 2x^2y^2 + y^4 - 4x^2y^2`
`= x^4 + y^4 - 2x^2y^2`
`b,`
`2(x - y)(x + y) + (x + y)^2 + (x - y)^2`
`= 2(x^2 - y^2) + x^2 + 2xy + y^2 + x^2 - 2xy + y^2`
`= 2x^2 - 2y^2 + 2x^2 + 2y^2`
`= 4x^2`
`c,`
`2(x - 1)^2 - 4(3 + x)^2 + 2x(x - 5)`
`= 2(x^2 - 2x + 1) - 4(9 + 6x + x^2) + 2x^2 - 10x`
`= 2x^2 - 4x + 2 - 36 - 24x - 4x^2 + 2x^2 - 10x`
`= (2x^2 - 4x^2 + 2x^2) + (-4x -24x - 10x) + (2 - 36)`
`= -38x - 34`
`d,`
`2(2x + 5)^2 - 3(4x + 1)(4x - 1)`
`= 2(4x^2 + 20x + 25) - 3(16x^2 - 1)`
`= 8x^2 + 40x + 50 - 48x^2 + 3`
`= -40x^2 + 40x + 53`
`5,`
`a,`
`(2x + 1)^2 - 4(x + 2)^2 = 9`
`=> 4x^2 + 4x + 1 - 4(x^2 + 4x + 4) = 9`
`=> 4x^2 + 4x + 1 - 4x^2 - 16x - 16 = 9`
`=> (4x^2 - 4x^2) + (4x - 16x) + (1 - 16) = 9`
`=> -12x - 15 = 9`
`=> -12x = 24`
`=> x = -2`
Vậy, `x = -2`
`b,`
`(20 - 2x)^2 = 256`
`=> (20 - 2x)^2 = +-16^2`
\(\Rightarrow\left[{}\begin{matrix}20-2x=16\\20-2x=-16\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=20-16\\2x=20-\left(-16\right)\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=4\\2x=36\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=18\end{matrix}\right.\)
Vậy, `x \in {2; 18}.`
`4,`
- Bài này bạn sử dụng các HĐT để làm bài nhé, mình gợi ý 1 số:
`A^2 - B^2 = (A - B)(A + B)`
`(A - B)^2 = A^2 - 2AB + B^2`
(Mình làm 1 số vd thui, chứ mình sắp đi học rồi =))
`39*41 = (40 - 1)(40 + 1) = 40^2 - 1^2 = 1600 - 1 = 1599`
`101^2 = (100 + 1)^2 = 100^2 + 2*100*1 + 1^2 = 10000 + 200 + 1 = 10201`
Mn giải giúp mik vs ạ 🥺 mình đang cần gấp. Cảm ơn mn nhiều