a) \(A=\left(5x+2y\right)^2\)
\(=\left(5x\right)^2+2\cdot5x\cdot2y+\left(2y\right)^2\)
\(=25x^2+20xy+4y^2\)
b) \(B=\left(4x-y\right)^2\)
\(=\left(4x\right)^2-2\cdot4xy+y^2\)
\(=16x^2-8xy+y^2\)
c) \(C=9x^2-25\)
\(=\left(3x-5\right)\left(3x+5\right)\)
d) \(D=\left(x+2\right)^3\)
\(=x^3+3x^2\cdot2+3x\cdot2^2+2^3\)
\(=x^3+6x^2+3x\cdot4+8\)
\(=x^3+6x^2+12x+8\)
a, \(A=\left(5x+2y\right)^2=25x^2+20xy+4y^2\)
b, \(B=\left(4x-y\right)^2=16x^2-8xy+y^2\)
c, \(C=9x^2-25=\left(3x-5\right)\left(3x+5\right)\)
d, \(D=\left(x+2\right)^3=x^3+6x^2+12x+8\)
e, \(E=\left(3x-1\right)^3=27x^3-9x^2+9x-1\)
g, \(G=x^3+64=\left(x+4\right)\left(x^2-4x+16\right)\)
h, \(H=27x^3-1=\left(3x-1\right)\left(9x^2+3x+1\right)\)
e) \(E=\left(3x-1\right)^3\)
\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2-1^3\)
\(=27x^3-3\cdot9x^2\cdot1+3\cdot3x\cdot1-1\)
\(=27x^3-27^2+9x-1\)
g) \(G=x^3+64\)
\(=\left(x+4\right)\left(x^2-4x+16\right)\)
h) \(H=27x^3-1\)
\(=\left(3x-1\right)\left(9x^2+3x+1\right)\)
\(a,A=\left(5x+2y\right)^2=\left(5x\right)^2+2.5x.2y+\left(2y\right)^2=25x^2+20xy+4y^2\)\(b,B=\left(4x-y\right)^2=\left(4x\right)^2-2.4x.y+y^2=16y^2-8xy+y^2\)\(c,C=9x^2-25=\left(3x\right)^2-5^2=\left(3x+5\right)\left(3x-5\right)\)\(d,D=\left(x+2\right)^3=x^3+6x^2+12x+8\)\(e,E=\left(3x-1\right)^3=27x^3-27x^2+9x-1\)\(g,G=x^3+64=x^3+4^3=\left(x+4\right)\left(x^2-4x+16\right)\)\(h,H=27x^3-1=\left(3x\right)^3-1=\left(3x-1\right)\left(9x^2+3x+1\right)\)
a) A=(5x+2y)2
= (5x)2 + 2.5x.2y + (2y)2
= 25x2 + 20xy + 4y2
b) B= (4x-y)2
= (4x)2 - 2.4x.y + y2
= 16x2 - 8xy + y2
c) C=9x2 - 25 = (3x)2 - 52 = (3x+5)(3x-5)
d)D=(x+2)3 = x3 + 3.x2.2 + 3.x.22 + 23 = x3 +6x2 + 12x + 8
e) E= (3x-1)3 = (3x)3 - 3.x2.1 + 3.x.12 - 13 = 27x3 + 3x2 +3x - 1
g)G=x3 + 64 = (x+4)(x2+4x+42) = (x+4)(x2 -4x +16)
h) H=27x3 - 1 = (3x-1)(9x2+3x+1)
