Question

Drag the tiles to the boxes to form correct pairs. Simplify each expression, and then make changes the equivalent expressions.

Answer 1

4(2x^2+3y^2)^2 = 16x^4 + 48x^2y^2 + 36y^4

(4x-5)(16x^2 + 20x + 25) = 64x^3 - 125

4 ( 2x^2 + 3y^2)(2x^2 - 3y^2) = 16x^4 -36y^4

hope that helps

Answer 2

`64x^3-125` ≡
`(4x-5)(16x^2+20x+25)`

`4(2x^2+3y^2)^2` ≡
`16x^4+36y^4+48x^2y^2`

`4(2x^2+3y^2)(2x^2-3y^2)` ≡
`16x^4-36y^4`

Step-by-step explanation :

(a) The given expression is:

`64x^3-125`

`=(4x)^3-(5)^3`

Using identity :
`a^3-b^3=(a-b)(a^2+2ab+b^2)`

`=(4x-5)(16x^2+20x+25)`

(b) The given expression is:

`4(2x^2+3y^2)^2`

Using identity :
`(a+b)^2=a^2+2ab+b^2`

`=4[(2x^2)^2+(3y^2)^2+2(2x^2)(3y^2)]`

`=4[4x^4+9y^4+12x^2y^2]`

`=16x^4+36y^4+48x^2y^2`

(c) The given expression is:

`4(2x^2+3y^2)(2x^2-3y^2)`

Using identity :
`(a+b)(a-b)=a^2-b^2`

`=4[(2x^2)^2-(3y^2)^2]`

`=4[4x^4-9y^4]`

`=16x^4-36y^4`