Question

Answer 1

`#3107`

`1)`

`4x^2 + 32x + 64`

`= (2x)^2 + 2*2x*8 + 8^2`

`= (2x + 8)^2`

`2)`

`x^2 - 14x + 49`

`= x^2 - 2*x*7 + 7^2`

`= (x - 7)^2`

`3)`

`9x^2 - 4`

`= (3x)^2 - 2^2`

`= (3x - 2)(3x + 2)`

`4)`

`27x^3 + y^3`

`= (3x)^3 + y^3`

`= (3x + y)(9x^2 - 3xy + y^2)`

`5)`

`8x^3 - 1/125 y^3`

`= (2x)^3 - (1/5y)^3`

`= (2x - 1/5y)(4x^2 + 2/5xy + 1/25y^2)`

`6)`

`-x^3 + 6x^2y - 12xy^2 + 8y^3`

`= -(x^3 - 6x^2y + 12xy^2 - 8y^3)`

`= -[(x)^3 - 3*x^2*2y + 3*x*(2y)^2 - (2y)^3]`

`= -(x - 2y)^3`

Answer 2

1) 4x² + 32x + 64

= 4(x² + 8x + 16)

= 4(x² + 2.x.4 + 4²)

= 4(x + 4)²

2) x² - 14x + 49

= x² - 2.x.7 + 7²

= (x - 7)²

3) 9x² - 4

= (3x)² - 2²

= (3x - 2)(3x + 2)

4) 27x³ + y³

= (3x)³ + y³

= (3x + y)[(3x)² - 3x.y + y²]

= (3x + y)(9x² - 3xy + y²)

5) 8x³ - 1/125 y³

= (2x)³ - (y/5)³

= (2x - y/5)[(2x)² + 2x.y/5 + (y/5)²]

= (2x - y/5)(4x² + 2xy/5 + y²/25)

6) -x³ + 6x²y - 12xy² + 8y³

= -[x³ - 3.x².2y + 3.x.(2y)² - (2y)³]

= -(x - 2y)³

= (y - 2x)³

Answer 3

1)

`4x^2+32x+64`

`=4(x^2+8x+16)`

`=4(x+4)^2`

2)

`x^2-14x+49`

`=(x-7)^2`

3)

`9x^2-4`

`=(3x-2)(3x+2)`

4)

`27x^3+y^3`

`=(3x)^3+y^3`

`=(3x+y)(9x^2-3xy+y^2)`

5)

`8x^3-1/125y^3`

`=(2x)^3-(1/5y)^3`

`=(2x-1/5y)(4x^2+2/5xy+1/25y^2)`

6)

`-x^3+6x^2y-12xy^2+8y^3`

`=-(x^3-6x^2y+12xy^2-8y^3)`

`=-(x-2y)^3`