49.(y - 4)^2 - 9.(y+2^2
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49(y-4)2 - 9(y+2)2
49(y-4)2 - 9(y+2)2
\(49\left(y-4\right)^2-9\left(y+2\right)^2=7^2.\left(y-4\right)^2-3^2.\left(y+2\right)^2\)
\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)
\(=\left(7y-28+3y+6\right).\left(7y-28-3y-6\right)\)
\(=4.\left(5y-11\right).\left(2y-17\right)\)
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\(49\left(y-4\right)^2-9\left(y+2\right)^2=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)=\left(4y-34\right)\left(10y-22\right)\)
\(=4\left(2y-17\right)\left(5y-11\right)\)
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49(y-4)2 - 9(y+2)2
49( y - 4 )2 - 9 ( y + 2 )2
= 72 ( y - 4 )2 - 32 ( ( y + 2 )2
= [ 7 ( y - 4 ) ]2 - [ 3 ( y + 2 ) ]2
= ( 7y - 4 )2 - ( 3y + 2 )2
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a, 9(x+5)2-(x-7)2
b, 49(y-4)2-9(y-2)2
a.\(9.\left(x+5\right)^2-\left(x-7\right)^2\)
\(=3^2.\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left(x+8\right)^2-\left(x-7\right)^2\)
\(=\left(x+8-x+7\right)\left(x+8+x-7\right)\)
\(=15\left(2x+1\right)\)
\(=30x+15\)
b.\(49\left(y-4\right)^2-9\left(y-2\right)^2\)
\(=7^2.\left(y-4\right)^2-3^2\left(y-2\right)^2\)
\(=\left(y+3\right)^2-\left(y+1\right)^2\)
\(=\left(y+3-y-1\right)\left(y+3+y+1\right)\)
\(=2\left(2y+4\right)\)
\(=4y+8\)
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a./ \(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2=\left(3x+15-x+7\right)\left(3x+15+x-7\right)=\left(2x+22\right)\left(4x+8\right).\)
\(=8\left(x+11\right)\left(x+2\right).\)
b./ \(=\left[7\left(y-4\right)\right]^2-\left[3\left(y-2\right)\right]^2=\left(7y-28+3y-6\right)\left(7y-28-3y+6\right)=\left(10y-34\right)\left(4y-22\right)\)
\(=4\left(5y-17\right)\left(2y-11\right)\)
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phân tích
49*(y-4)^2 -9*(y+2)^2
9*(x+5)-(x+7)2
3x*(x-1)^2 -5x*(x+1)+7*(x+2)
phần tích đa thức thành nhân tử
a) 9(x+5) ^2 -(x-7)^2
b) 25(x-y)^2 - 16(x+y)^2
c)49(y-4)^2 - 9(y+2)^2
d) x^4 + x^3 +x +1
e) x^4 - x^3 - x^2 +1
phân tích đa thức thành nhân tử: 49(y-4)^2-9(y+2)^2
\(49\left(y-4\right)^2-9\left(y+2\right)^2\)
\(=7^2\left(y-4\right)^2-3^2\left(y+2\right)^2\)
\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2\)
\(=\left[7\left(y-4\right)-3\left(y+2\right)\right]\left[7\left(y-4\right)+3\left(y+2\right)\right]\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)
\(=\left(4y-34\right)\left(10y-22\right)\)
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`49(y-4)²-9(y+2)²`
`= [7(y-4)]²-[3(y+2)]²`
`= [7(y-4)+3(y+2)]-[7(y-4)-3(y+2)]`
`= (7y-28+3y+6)(7y-28-3y-6)`
`= (10y-22)(4y-34)`
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tìm x, y biết :
a) ( 3x - 5 ) ( 5 - 3x ) + 9 ( x + 1 )^2 = 30
b) ( x + 4 )^2 - ( x + 1 ) ( x - 1 ) = 16
c) ( y - 2 )^3 - ( y - 3 ) ( y^2 + 3y + 9 ) + 6 ( y + 1 )^2 = 49
d ) ( y + 3 )^3 - ( y + 1 )^3 = 56
a) \(\left(3x-5\right)\left(5-3x\right)+9\left(x+1\right)^2=30\)
\(\Rightarrow15x-9x^2-25+15x+9\left(x^2+2x+1\right)-30=0\)
\(\Rightarrow30x-9x^2-25+9x^2+18x+9-30=0\)
\(\Rightarrow48x-46=0\)
\(\Rightarrow x=\frac{23}{24}\)
b) \(\left(x+4\right)^2-\left(x+1\right)\left(x-1\right)=16\)
\(\Rightarrow\left(x^2+8x+16\right)-\left(x^2-1\right)=16\)
\(\Rightarrow x^2+8x+16-x^2+1=16\)
\(\Rightarrow8x+17=16\)
\(\Rightarrow8x=-1\)
\(\Rightarrow x=\frac{-1}{8}\)
c) \(\left(y-2\right)^3-\left(y-3\right)\left(y^2+3y+9\right)+6\left(y+1\right)^2=49\)
\(\Rightarrow\left(y-2\right)^3-\left(y^3-3^3\right)+6\left(y^2+2y+1\right)=49\)
\(\Rightarrow y^3-6y^2+12y-8-y^3+27+6y^2+12y+6=49\)
\(\Rightarrow\left(y^3-y^3\right)+\left(-6y^2+6y^2\right)+\left(12y+12y\right)+\left(-8+27+6\right)=49\)
\(\Rightarrow24y+25=49\)
\(\Rightarrow24y=24\)
\(\Rightarrow y=1\)
d) \(\left(y+3\right)^3-\left(y+1\right)^3=56\)
\(\Rightarrow\left(y+3-y-1\right)[\left(y+3\right)^2+\left(y+3\right)\left(y+1\right)+\left(y+1\right)^2]=56\)
\(\Rightarrow2\left(y^2+6y+9+y^2+4y+3+y^2+2y+1\right)=56\)
\(\Rightarrow3y^2+12y+13=28\)
\(\Rightarrow\left(3y^2+15y\right)-\left(3y+15\right)=0\)
\(\Rightarrow3y\left(y+5\right)-3\left(y+5\right)=0\)
\(\Rightarrow3\left(y-1\right)\left(y+5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x+5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=-5\end{cases}}\)
1)
a) (x+5)^2-(x-7)^2
b) 49(y-4)^2-9(y+2)^2
2)
a)16x^2-9=0
(giai bang 3 cach)