Question

help me 

Answer 1

Bài 8:

\(a,\left(6-x\right)^2=36-12x^2+x^2\\ \left(x-5\right)^2=x^2-10x+25\\ \left(5x+1\right)^2=25x^2+10x+1\\ \left(2x-1\right)^2=4x^2-4x+1\\ \left(2x+3\right)^2=4x^2+12x+9\\ \left(3+2x\right)^2=9+12x+4x^2\\b, x^2-4=\left(x-2\right)\left(x+2\right)\\ 1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\\ 4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\\ 9-25x^2=3^2-\left(5x\right)^2=\left(3-5x\right)\left(3+5x\right)\\ 4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\\ 9x^2-36=9\left(x^2-4\right)=9\left(x-2\right)\left(x+2\right)\)

Answer 2

\(b2:\\ a,4x^4-4x^2+1=\left(2x^2\right)^2-2.2x^2.1+1^2=\left(2x^2-1\right)^2=\left(1-2x^2\right)^2\\ ---\\ 36+x^2-12x\\ =6^2-2.6.x+x^2=\left(6-x\right)^2=\left(x-6\right)^2\\ ---\\ 4x^2-12x+9=\left(2x\right)^2-2.2x.3+3^2=\left(2x-3\right)^2=\left(3-2x\right)^2\\ ---\\ 1-10x+25x^2=1^2-2.1.5x+\left(5x\right)^2=\left(1-5x\right)^2=\left(5x-1\right)^2\\ ---\\ x^4+81+18x^2=\left(x^2\right)^2+2.x^2.9+9^2=\left(x^2+9\right)^2\)

\(x^2+4y^4-4xy^2=x^2-2.x.2y^2+\left(2y^2\right)^2=\left(x-2y^2\right)^2=\left(2y^2-x\right)^2\\---\\ x^2+10xy+25y^2=x^2+2.x.5y+\left(5y\right)^2=\left(x+5y\right)^2\\ ---\\ 9y^2-24xy+16x^2=\left(3y\right)^2-2.3y.4x+\left(4x\right)^2=\left(3y-4x\right)^2=\left(4x-3y\right)^2\\ ---\\ 16x^2+9y^4+24xy^2=\left(4x\right)^2+\left(3y^2\right)^2+2.4x.3y^2=\left(4x+3y^2\right)^2\)

Answer 3

\(Bài.2:\\ b,\left(x+2y\right)^2=x^2+2.x.2y+\left(2y\right)^2=x^2+4xy+4y^2\\ ---\\ \left(x+5y\right)^2=x^2+2.x.5y+\left(5y\right)^2=x^2+10xy+25y^2\\ ---\\ \left(x-2y\right)^2=x^2-2.x.2y+\left(2y\right)^2=x^2-4xy+4y^2\\ ---\\ \left(3x+5y\right)^2=\left(3x\right)^2+2.3x.5y+\left(5y\right)^2=9x^2+30xy+25y^2\\ ---\\ \left(3y-4x\right)^2=\left(3y\right)^2-2.3y.4x+\left(4x\right)^2=9y^2-24xy+16x^2\\ ---\\ \left(2x-5y\right)^2=\left(2x\right)^2-2.2x.5y+\left(5y\right)^2=4x^2-20xy+25y^2\\ ---\\ \left(2x+3y\right)^2=\left(2x\right)^2+2.2x.3y+\left(3y\right)^2=4x^2+12xy+9y^2\\ ---\\ \left(3x-5y\right)^2=\left(3x\right)^2-2.3x.5y+\left(5y\right)^2=9x^2-30xy+25y^2\\ ---\\ \left(2x-3y\right)^2=\left(2x\right)^2-2.2x.3y+\left(3y\right)^2=4x^2-12xy+9y^2\)

Answer 4

\(Bài.2:\\ c,\left(x^2-y^2\right)^2=\left(x^2\right)^2-2x^2y^2+\left(y^2\right)^2=x^4-2x^2y^2+y^4\\ ---\\c, \left(x^2+3^2\right)^2=\left(x^2+9\right)^2=\left(x^2\right)^2+2.x^2.9+9^2=x^4+18x^2+81\\ c,\left(2x^2+1\right)^2=\left(2x^2\right)^2+2.2x^2.1+1^2=4x^4+4x^2+1\\c, \left(3x-y^2\right)^2=\left(3x\right)^2-2.3x.y^2+\left(y^2\right)^2=9x^2-6xy^2+y^4\\ c,\left(x+2y^2\right)^2=x^2+2.x.2y^2+\left(2y^2\right)^2=x^2+4xy^2+4y^4\)

\(c,\left(3x\right)^2-y^2=\left(3x-y\right)\left(3x+y\right)\\ c,\left(2x+3y^2\right)^2=\left(2x\right)^2+2.2x.3y^2+\left(3y^2\right)^2=4x^2+12xy^2+9y^4\\ c,\left(4x-2y^2\right)=\left(4x\right)^2-2.4x.2y^2+\left(2y^2\right)^2=16x^2-16xy^2+4y^4\\ c,\left(4x^2-2y\right)^2=\left(4x^2\right)^2-2.4x^2.2y+\left(2y\right)^2=16x^4-16x^2y+4y^2\)