embizze | High School Teacher | (Level 1) Educator Emeritus

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(1) `125s^6+8g^3` recognize as the sum of cubes: `a^3+b^3=(a+b)(a^2-ab+b^2)`

`125s^6+8g^3=(5s^2)^3+(2g)^3`

`=(5s^2+2g)(5s^2)^2-5s^2 2g+(2g)^2)`

`=(5s^2+2g)(25s^4-10s^2g+4g^2)`

(2) 64x^4-4y^4 recognize as the difference of two squares: `a^2-b^2=(a+b)(a-b)`

`64x^4-4y^4=(8x^2)^2-(2y^2)^2`

`=(8x^2-2y^2)(8x^2+2y^2)`  The first term factors:

`=2(4x^2-y^2)2(4x^2+y^2)`  as a difference of two squares

`=4(2x+y)(2x-y)(4x^2+y^2)`

(3) `75b^3c-12bc^3` factor out the greatest common factor

`=3bc(25b^2-4c^2)` recognize the difference of two squares:

`=3bc(5b+2c)(5b-2c)`

(4) Factor out the common factor pairwise:

`4xz+12x+5yz+15y`

`=4x(z+3)+5y(z+3)`  The binomial factor is a common factor

`=(z+3)(4x+5y)`

oldnick | (Level 1) Valedictorian

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`125s^6+8g^3=(5s^2+2g)(25s^4-10s^2g+4g^2)`

`64x^4-4y^4=4(16x^4-y^4)=4(4x^2-y^2)(4x^2+y^2)=`

`=4(4x^2+y^2)(2x+y)(2x-y)`

`75b^3c - 12bc^3=3bc(25b^2-4c^2)=3bc(5b-2c)(5b+2c)`

`4xz+12x+5yz+15y` `=4x(z+3)+5y(z+3)=(4x+5y)(z+3)`