Answer:
The pair of equivalent expressions are 2 and 8, 3 and 7, 4 and 5.
Step-by-step explanation:
Expand or factor each of the following expressions
1.
[tex](4x-3y)^2=(4x)^2-(2(4x)(3y)+(3y)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex](4x-3y)^2=16x^2-24xy+9y^2[/tex]
2.
[tex]9x^2+3x-20=9x^2+15x-12x-20[/tex]
[tex]9x^2+3x-20=3x(3x+5)-4(3x+5)[/tex]
[tex]9x^2+3x-20=(3x+5)(3x-4)[/tex]
It is same as expression 8. Therefore expression 2 and 8 are equivalent.
3.
[tex](3x-2)(9x^2+6x+4)=(3x-2)((3x)^2+(3x(2)+2^2)[/tex]
[tex](3x-2)(9x^2+6x+4)=(3x)^3-(2)^3[/tex] [tex][\because a^3-b^3=(a-b)(a^2+ab+b^2)][/tex]
[tex](3x-2)(9x^2+6x+4)=27x^3-8[/tex]
It is same as expression 7. Therefore expression 3 and 7 are equivalent.
4.
[tex]9x^2-24xy+16y^2=(3x)^2-2(3x)(4y)+(4y)^2[/tex]
[tex]9x^2-24xy+16y^2=(3x-4y)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
It is same as expression 5. Therefore expression 4 and 5 are equivalent.
5.
[tex](3x-4y)^2=9x^2-24xy+16y^2[/tex]
6.
[tex](3x+2)(9x^2-6x+4)=(3x+2)((3x)^2-(3x(2)+2^2)[/tex]
[tex](3x+2)(9x^2-6x+4)=(3x)^3+(2)^3[/tex] [tex][\because a^3+b^3=(a+b)(a^2-ab+b^2)][/tex]
[tex](3x+2)(9x^2-6x+4)=27x^3+8[/tex]
7.
[tex]27x^3-8=(3x-2)(9x^2+6x+4)[/tex]
8.
[tex](3x+5)(3x-4)=9x^2+3x-20[/tex]
Therefore the pair of equivalent expressions are 2 and 8, 3 and 7, 4 and 5.
