Question

Replace ∗ with a monomial so that the result is an identity:

Answer 1

Answer:

Each of these is based on the principle of difference of two squares where:

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

Step-by-step explanation:

1.$(2a + *)(2a - *) = 4a^2-b^2$

$4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)$

2. $(*- 3x )(*+3x) = 16y^2-9x^2$

$16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)$

3. $100m^4-4n^6 = (10m^2-*)(*+10m^2)$

$100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)$

4. $m^4-225c^{10} = (m^2-*)(* +m^2)$

$m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)$