Question

Answer 1

a: \(=8x^3-60x^2+150x-125-6\left(x^3-8\right)-4x^3+3x\)

\(=4x^3-60x^2+153x-125-6x^3+48\)

\(=-2x^3-60x^2+153x-77\)

b: \(=x^4+6x^2y+9y^2-4x^2\left(x^4-y^2\right)\)

\(=x^4+6x^2y+9y^2-4x^6+4x^2y^2\)

Answer 2

a) (2x - 5)³ - 6(x - 2)(x² + 2x + 4) - x(4x² - 3)

= (2x)³ - 3.(2x)².5 + 3.2x.5² - 5³ - 6(x³ - 2³) - 4x³ + 3x

= 8x³ - 60x² + 150x - 125 - 6x³ + 48 - 4x³ + 3x

= -2x³ + 60x² + 153x - 77

Answer 3

`(a):(2x-5)^{3}-6(x-2)(x^{2}+2x+4)-x(4x^{2}-3)`

`=(2x)^{3}-3.(2x)^{2}.5+3.2x.5^{2}-5^{3}-6(x^{3}-2^{3})-4x^{3}+3x`

`=8x^{3}-60x^{2}+150x-125-6x^{3}+48-4x^{3}+3x`

`=-2x^{3}-60x^{2}+153x-77`

`(b):(x^{2}+3y)^{2}-4x^{2}(y+x^{2})(x^{2}-y)`

`=(x^{2})^{2}+2.x^{2}.3y+(3y)^{2}-4x^{2}(x^{4}-y^{2})`

`=x^{4}+6x^{2}y+9y^{2}-4x^{6}+4x^{2}y^{2}`

 

Answer 4

\(a,=8x^3-60x^2+150x-125-6\left(x^3-8\right)-4x^3+3x\\ =4x^3-60x^2+153x-125-6x^3+48\\ =-2x^3-60x^2+153x-77\\ b,=x^4+6x^2y+9y^2-4x^2\left(x^4-y^2\right)\\ =x^4+6x^2y+9y^2-4x^6+4x^2y^2\)

Answer 5

b) (x² + 3y)² - 4x²(y + x²)(x² - y)

= x⁴ + 6x²y + 9y² - 4x²(x⁴ - y²)

= x⁴ + 6x²y + 9y² - 4x⁶ + 4x²y²