Question

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

Answer 1

Answer :

$64x^3-125$ ≡ $(4x-5)(16x^2+20x+25)$

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

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

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 : $(a+b)(a-b)=a^2-b^2$

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

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

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

Answer 2

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