Answer:
Each of these is based on the principle of difference of two squares where:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Step-by-step explanation:
1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]
[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]
2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]
[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]
3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]
[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]
4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]
[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]
