Question

Can I have help with 43 and 44 I need to see how to do them thanks.

Answer 1

1. 3x^5 -75x³

=3x³(x²-25)

=3x³(x²-5²)

=3x³(x-5)(x+5)

2. 81c²+72c+16

=81c²+36c+36c+16

=9c(9c+4)+4(9c+4)

=(9c+4)(9c+4)

=(9c+4)²

Answer 2

see explanation

Explanation:

(43)

3
`x^(5)` - 75x³ ← factor out 3x³ from each term

= 3x³(x² - 25) ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , thus

x² - 25 = x² - 5² = (x - 5)(x + 5)

Thus

3
`x^(5)` - 75x³ = 3x³(x - 5)(x + 5)

(44)

81c² + 72c + 16 ← is a perfect square of the form

(ac + b)² = a²c² + 2abc + b²

Compare coefficients of like terms

a² = 81 ⇒ a =
`√(81)` = 9

b² = 16 ⇒ b =
`√(16)` = 4

and 2ab = 2 × 9 × 4 = 72

Thus

81c² + 72c + 16 = (9c + 4)²