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Bạn áp dụng hằng đẳng thức \(a^2+2ab+b^2=\left(a+b\right)^2\)
Khi đó\(a=x^2+1\)
\(b=x^2+6x-1\)
\(\left(x-3\right)\left(x+3\right)-\left(x-3\right)^2\)
\(=x^2-3^2-x^2+6x-3^2\)
\(=-9-9+6x\)
\(=6x-18\)
1 )
\(\left(x-3\right)\left(x+3\right)-\left(x-3\right)^2\)
\(=x^2-3^2-\left[x^2-3x-3x+9\right]\)
\(=x^2-9-x^2+6x-9\)
\(=6x-18\)
2 )
\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(6x+1\right)\left(6x-1\right)\)
\(=\left(6x\right)^2+2.6x.1+1+\left(6x\right)^2-2.6x.1+1-2\left[\left(6x\right)^2-1^2\right]\)
\(=36x^2+12x+1+36x^2-12x+1-2\left(36x^2-1\right)\)
\(=72x^2+1+1-72x^2+2\)
\(=4\)
\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(=\left[\left(6x+1\right)-\left(6x-1\right)\right]^2\)
\(=\left(6x+1-6x+1\right)^2\)
\(=2^2\)
\(=4\)
a) Ta có:(6x+1)^2 +(6x-1)^2 +2(6x+1)(6x-1) =[(6x+1)+(6x-1)]^2 =(12x)^2=(12^2)(x^2)=144.x^2
b) Ta có:(6x+1)^2 +(6x-1)^2 -(12x+2)(6x-1)=(6x+1)^2 +(6x-1)^2 -2(6x+1)(6x-1)=[(6x+1)-(6x-1)]^2=2^2=4
c) Ta có:(ac+bd)^2 +(ad-bc)^2=(ac)^2 +2(ac)(bd) +(bd^2) +(ad)^2 -2(ad)(bc) +(bc)^2
=a^2.c^2 +2abcd +b^2 d^2 +a^2.d^2 -2abcd +b^2.c^2=a^2.c^2 +b^2.d^2 +a^2.d^2 +b^2.c^2
=(a^2 +b^2)(c^2 +d^2)
d) Ta có:(ac-bd)(ac+bd)=(ac)^2 -(bd)^2=a^2.c^2 -b^2.d^2
\(x^3+8x^2+17x+10\)
\(=x^3+2x^2+x^2+5x^2+10x+5x+2x+10\)
\(=\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(5x^2+5x\right)+\left(10x+10\right)\)
\(=x^2\left(x+1\right)+2x\left(x+1\right)+5x\left(x+1\right)+10\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+2x+5x+10\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+5\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+5\right)\)
\(=\left(6x+1\right)^2-2\cdot\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2.\)
\(=\left(6x+1-\left(6x-1\right)\right)^2=2^2=4.\)
(6x+1)^2+(6x-1)^2-2(1+6x)*(6x-1)
=(6x+1)2-2(6x+1)(6x-1)+(6x-1)2
=[(6x+1)-(6x-1)]2
=(6x+1-6x+1)2
=22
=4
\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(\Rightarrow\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)
\(\Rightarrow\left(6x+1-6x+1\right)^2\)
\(\Rightarrow2^2\)
\(\Rightarrow4\)
Cái này là tính chất giao hoán của phép cộng á bạn
A+B+C=A+C+B