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bài 1
a, \(\left(3x-2\right)^2=9x^2-12x+4\)
b,\(\left(5-3t\right)^2=25-30t+9t^2\)
c, \(\left(y-5\right)\left(y+5\right)=y^2-25\)
d, \(\left(3-x^2\right)^2=9-6x^2+x^4\)
e, \(\left(a^2+\frac{3}{5}b\right)\left(a^2-\frac{3}{5}b\right)=a^4-\frac{9}{25}b^2\)
q,\(15\left(-\frac{1}{4}x+\frac{4}{5}v\right)^2=15\left(\frac{1}{16}x^2-\frac{1}{5}xv+\frac{16}{25}v^2\right)\)
\(=\frac{15}{16}x^2-3xv+\frac{15.16}{25}v^2\)
bài 2 : câu a sửa đề thành +1 thôi
a, \(16u^2v^4-8uv^2+1=\left(4uv^2\right)^2-2.\left(4uv^2\right)+1^2=\left(4uv^2-1\right)^2\)
b,\(4x^2-4x+1=\left(2x\right)^2-2.2x+1=\left(2x-1\right)^2\)
c, \(\frac{x^2}{4}-3x+4=\left(\frac{x}{2}\right)^2-2.\frac{x}{2}.3+3^2-5\)
\(=\left(\frac{x}{2}-3\right)^2-\sqrt{5}^2=\left(\frac{x}{2}-3-\sqrt{5}\right)\left(x^2-3+\sqrt{5}\right)\)
d, \(\left(2n-m\right)^2+2\left(2n-m\right)+1=\left(2n-m+1\right)^2\)
e, \(23v^2-10v+1=\left(5v\right)^2-2.5v+1-2v^2\)
\(=\left(5v-1\right)^2-\left(\sqrt{2}v\right)^2=\left(5v-1-\sqrt{2}v\right)\left(5v-1+\sqrt{2}v\right)\)
g, \(x^2+10x+25=\left(x+5\right)^2\)
Bài 1 : \(a,\)\(16u^2v^4-8uv^2+1\)
\(=\left(4uv^2\right)^2-2.4uv^2.1+1^2\)
\(=\left(4uv^2-1\right)^2\)
\(b,\)\(4x^2-12x+4\)
\(\left(2x\right)^2-2.2x.3+3^2-5\)
\(=\left(2x-3\right)^2-\left(\sqrt{5}\right)^2\)
\(=\left(2x-3-\sqrt{5}\right)\left(2x-3+\sqrt{5}\right)\)
Bài 2 :
\(\left(x+1-2y\right)^2\)
\(=\left[\left(x-1\right)-2y\right]^2\)
\(=\left(x-1\right)^2-2\left(x-1\right).2y+\left(2y\right)^2\)
\(=x^2-2x+1-4xy+4y+4y^2\)
Bài 3 : ( Đề nhầm tí nha , coi lại nhé )
\(x^2+y^2=\left(x+y\right)^2-2xy\)
\(\Rightarrow x^2+y^2=x^2+2xy+y^2\)
\(\Rightarrow x^2+y^2=x^2+y^2\) ( luôn đúng với \(\forall x\))
\(\Rightarrow x^2+y^2=\left(x+y\right)^2-2xy\)\(\left(đpcm\right)\)
b) \(3x\left(x-1\right)^2-2x\left(x+3\right)\left(x-3\right)+4x\left(x-4\right)\)
\(=3x\left(x^2-2x+1\right)-2x\left(x^2-9\right)+4x^2-16x=3x^3-6x^2+3x-2x^3+18x+4x^2-16x\)\(=x^3-2x^2+5x\)
c) \(2\left(2x+5\right)^2-3\left(4x+1\right)\left(1-4x\right)=2\left(4x^2+20x+25\right)+3\left(16x^2-1\right)\)
\(=8x^2+40x+50+48x^2-3=56x^2+40x+47\)
d) \(x\left(x+4\right)\left(x-4\right)-\left(x^2+1\right)\left(x^2-1\right)=x\left(x^2-16\right)-x^4+1=x^3-x^4-16x+1\)
e) \(\left(y-3\right)\left(y+3\right)\left(y^2+9\right)-\left(y^2+2\right)\left(y^2-2\right)=\left(y^2-9\right)\left(y^2+9\right)-y^4+4=y^4-81-y^2+4=-77\)
bạn phải tách từng câu ra. chứ kiểu này k ai trả lời cho đâu
2)
a)x2-y2=(x+y).(x-y)=(87+13).(87-13)=100.74=7400
b)x3-3x2+3x-1=(x-1)3=(101-1)3=1003=1000000
c)x3+9x2+27x+27=(x+3)3=(97+3)3=1003=1000000
4)
a)x2-6x+10=x2-6x+9+1=(x-3)2+1>=1>0 voi moi x
b)4x-x2-5= -(x2-4x+5)= -(x2-4x+4+1)= -(x-2)2 - 1<0 voi moi x
Bài 1 :
Áp dụng hằng đẳng thức giải nhé
Bài 2 :
g, \(x^2+10x+25=\left(x+5\right)^2\)
b, \(4x^2-4x+1=\left(2x-1\right)^2\)
Bài 3 :
\(81^2=\left(80+1\right)^2=80^2+1^2+2.80=6400+1+160\)
\(=6401+160=6561\)
Tương tự nhé !