Respuesta :
Answer:
-(3p +1) (p + 1); 5c(5c - 6 d); -9b(9b + 2a²)
Step-by-step explanation:
p² – (2p + 1)²
= p² - (4p² + 4p + 1)
= p² - 4p² - 4p - 1
= -3p² - 4p - 1
= -(3p² + 4p + 1)
= -(3p +1) (p + 1)
(5c – 3d)² – 9d²
= 25c² - 30cd + 9d² - 9d²
= 25c² - 30cd
= 5c(5c - 6 d)
a⁴ – (9b + a²)²
= a⁴ - (81b² + 18a²b + a⁴)
= a⁴ - 81b² - 18a²b - a⁴
= -81b² - 18a²b
= -9b(9b + 2a²)
Using the property of the multiplication to solve the preoblem, then the multiplications are -(3p² + 4p + 1), 5c(5c - 6d), and -9b(9b + 2a²).
What is multiplication?
It is also known as the product. If the object n is given to m times then we just simply multiply them.
Given
1. [tex]\rm p^2 - (2p + 1 )^2[/tex]
2. [tex]\rm (5c -3d )^2 - 9d^2[/tex]
3. [tex]\rm a^4 - (9b + a^2 )^2[/tex]
1. [tex]\rm p^2 - (2p + 1 )^2[/tex]
On multiplication
[tex]\rm p^2 - (2p + 1 )^2\\\\\rm p^2 - 4p^2 - 1 -4p \\\\ -3p^2 -1 -4p \\\\-(3p^2 + 4p+1)[/tex]
2. [tex]\rm (5c -3d )^2 - 9d^2[/tex]
On multiplication
[tex]\rm (5c -3d )^2 - 9d^2\\\\\rm 25c^2 + 9d^2 - 30cd - 9d^2\\\\25c^2 - 30cd\\\\5c(5c - 6d)[/tex]
3. [tex]\rm a^4 - (9b + a^2 )^2[/tex]
On multiplication
[tex]\rm a^4 - (9b + a^2 )^2\\\\\rm a^4 - a^4 -81b^2 -18a^2b \\\\ - 81b^2 - 18a^2b \\\\-9b(9b + 2a^2)[/tex]
Thus, the multiplications are -(3p² + 4p + 1), 5c(5c - 6d), and -9b(9b + 2a²).
More about the multiplication link is given below.
https://brainly.com/question/19943359
