4:
=>x^3-9x^2+27x-27-x^3+27+9(x^2+2x+1)=15
=>-9x^2+27x+9x^2+18x+9=15
=>45x=6
=>x=2/15
3:
a: A=(2025-1)(2025+1)=2025^2-1<2025^2=B
b: A=(3^2-1)(3^2+1)(3^4+1)
=(3^4-1)(3^4+1)
=3^8-1<3^8=B
1
a \(=\left(x+1\right)^2\)
b \(=\left(x-1\right)\left(x+1\right)\)
c \(=\left(x-3\right)^2\)
d \(=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)
e \(=\left(4x\right)^2-2.4x.1+1=\left(4x-1\right)^2\)
g \(=x^3+3^3=\left(x+3\right)\left(x^2-3x+9\right)\)
h \(=x^3+1\)
f \(=x^3-5^3=x^3-125\)
\(1.\)
\(a.x^2+2x+1=x^2+x+x+1=\left(x^2+x\right)+\left(x+1\right)=x\left(x+1\right)+x+1=\left(x+1\right)\left(x+1\right)\) \(=\left(x+1\right)^2\)
\(b.x^2-1=\left(x+1\right)\left(x-1\right)\)
\(c.x^2-6x+9\)
\(=x^2-3x-3x+9\)
\(=\left(x^2-3x\right)-\left(3x+9\right)\)
\(=x\left(x-3\right)-3\left(x-3\right)\)
\(=\left(x-3\right)\left(x-3\right)\)
\(=\left(x-3\right)^2\)
\(d.4x^2-9\)
\(=4x^2+6x-6x-9\)
\(=\left(4x^2+6x\right)-\left(6x-9\right)\)
\(=2x\left(2x+3\right)-3\left(2x+3\right)\)
\(=\left(2x+3\right)\left(2x-3\right)\)
\(e.16x^2-8x+1\)
\(=16x^2-4x-4x+1\)
\(=\left(16x^2-4x\right)+\left(-4x-1\right)\)
\(=4x\left(4x-1\right)-1\left(4x-1\right)\)
\(=\left(4x-1\right)\left(4x-1\right)\)
\(=\left(4x-1\right)^2\)
\(g.x^3+27=\left(x+3\right)\left(x^2-3x+9\right)\)
\(h.\left(x+1\right)\left(x^2-x+1\right)=x^3+1\)
\(f.\left(x-5\right)\left(x^2+5x+25\right)=x^3-125\)
