Question

Answer 1

g: \(\left(3x^2-2y\right)^3\)

\(=\left(3x^2\right)^3-3\cdot\left(3x^2\right)^2\cdot2y+3\cdot3x^2\cdot4y^2-8y^3\)

\(=27x^6-54x^4y+36x^2y^2-8y^3\)

h: \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-27y^3\)

i: \(\left(x^2-3\right)\cdot\left(x^4+3x^2+9\right)=x^6-27\)

m: \(\left(x+2\right)\left(x^2-2x+4\right)=x^3+8\)

n: \(\left(x-3\right)\left(x^2+3x+9\right)=x^3-27\)

Answer 2

n.

\(=\left(x-3\right)\left(x+3\right)^2=\left(x-3\right)\left(x+3\right)\left(x+3\right)\)

m.

\(=\left(x+2\right)\left(x-2\right)^2=\left(x+2\right)\left(x-2\right)\left(x-2\right)\)

Answer 3

g) \(\left(3x^2-2y\right)^3=\left(3x^2\right)^3-3.\left(3x^2\right)^2.2y+3.3x^2.\left(2y\right)^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36x^2y^2-8y^3\)

h) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

\(=x^3-\left(3y\right)^3\)

\(=x^3-27y^3\)

i) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)\)

\(=\left(x^2\right)^3-3^3\)

\(=x^6-27\)

Answer 4

j) \(\left(x+2y+z\right)\left(x+2y-z\right)\)

\(=\left[\left(x+2y\right)+z\right]\left[\left(x+2y\right)-z\right]\)

\(=\left(x+2y\right)^2-z^2\)

\(=x^2+4xy+4y^2-z^2\)

k) \(\left(2x-1\right)\left(4x^2+2x+1\right)\)

\(=\left(2x\right)^3-1^3\)

\(=8x^3-1\)

l) \(\left(5+3x\right)^3\)

\(=5^3+3.5^2.3x+3.5.\left(3x\right)^2+\left(3x\right)^3\)

\(=125+225x+135x^2+27x^3\)

Answer 5

m) \(\left(x+2\right)\left(x^2-2x+4\right)\)

\(=x^3+2^3\)

\(=x^3+8\)

n) \(\left(x-3\right)\left(x^2+3x+9\right)\)

\(=x^3-3^3\)

\(=x^3-27\)