1) \(B=5\left(2x-1\right)^2+4\left(x-1\right)\left(x+3\right)+2\left(5-3x\right)^2\)
\(=5\left(4x^2-4x+1\right)+\left(4x-4\right)\cdot\left(x+3\right)+2\left(25-30x+9x^2\right)\)
\(=20x^2-20x+5+4x^2+12x-4x-12+50-60+18x^2\)
\(=42x^2-72x+43\)
2) \(C=\left(2a^2+2a+1\right)\left(2a^2-2a+1\right)-\left(2a+1\right)^2\)
\(=4a^4-4a^3+2a^2+4a^3-4a^2+2a+2a^2-2a+1-\left(4a^2+4a+1\right)\)
\(=4a^4+2a^2-4a^2+2a^2+1-4a^2-4a-1\)
\(=4a^4-4a^2-4a\)
3) Sky Sơn Tùng làm đúng rồi nhé.
4) \(E=\left(x^2-5x+1\right)^2+2\left(5x-1\right)\left(x^2-5x+1\right)\left(5x-1\right)^2\)
\(=x^4+27x^2+1-10x^3+250x^5-1400x^4+1030x^3-302x^2+40x-2\)
\(=-1399x^4-275x^2-1+1020x^3+250x^5+40x\)
5) \(F=\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2\)
\(=\left[a^2+b^2-c^2-\left(a^2-b^2+c^2\right)\right]\cdot\left(a^2+b^2-c^2+a^2-b^2+c^2\right)\)
\(=\left(a^2+b^2-c^2-a^2+b^2-c^2\right)\cdot2a^2\)
\(=\left(2b^2-2c^2\right)\cdot2a^2\)
\(=2\left(b^2-c^2\right)\cdot2a^2\)
\(=2\left(b-c\right)\left(b+c\right)\cdot2a^2\)
\(=2\cdot2a^2\cdot\left(b-c\right)\left(b+c\right)\)
\(=4a^2\cdot\left(b-c\right)\left(b+c\right)\)
6) \(G=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
\(=a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+\left(-c\right)^2+2ab-2ac-2bc-2\left(a^2+2ab+b^2\right)\)
\(=a^2+b^2+c^2+2ab+a^2+b^2+\left(-c\right)^2+2ab-2a^2-4ab-2b^2\)
\(=0+0+c^2+0+c^2\)
\(=2c^2\)
7) \(H=\left(a+c\right)\left(a-c\right)-\left(a-b-c\right)\left(a-b+c\right)+b\left(b-2x\right)\)
\(=a^2-c^2-\left[\left(a-b\right)^2-c^2\right]+b^2-2bx\)
\(=a^2-c^2-\left(a^2-2ab+b^2-c^2\right)+b^2-2bx\)
\(=a^2-b^2-a^2+2ab-b^2+c^2+b^2-2bx\)
\(=2ab-2bx\)
