Question

A)144a4-625c2 б)25p10-1/9g12

Answer 1

$144a^4-625c^2=(12a^2)^2-(25c)^2=(12a^2-25c)(12a^2+25c)$

$25p ^{10} - \frac{1}{9} g ^{12} =(5p^5)^2-( \frac{1}{3} g^6)^2=(5p^5-\frac{1}{3} g^6)(5p^5+\frac{1}{3} g^6)$

Answer 2

a) To simplify the expression 144a^4-625c^2, we can use the difference of squares identity, which states that a^2 - b^2 = (a+b)(a-b). Here, we have (12a^2)^2 - (25c)^2, which can be written as:

(12a^2 + 25c)(12a^2 - 25c)

So, the simplified expression is:

144a^4 - 625c^2 = (12a^2 + 25c)(12a^2 - 25c)

b) To simplify the expression 25p^10 - (1/9)g^12, we can first note that 1/9 is equal to (1/3)^2. So we have:

25p^10 - (1/9)g^12 = 25p^10 - (1/3)^2 * g^12

Using the difference of squares identity again, we have:

(5p^5)^2 - [(1/3)g^6]^2

Which can be written as:

(5p^5 + (1/3)g^6)(5p^5 - (1/3)g^6)

So the simplified expression is:

25p^10 - (1/9)g^12 = (5p^5 + (1/3)g^6)(5p^5 - (1/3)g^6)