Step-by-step explanation:
#1.
(a + 2b)²
<em>Using identity (x + y)² = x² + 2xy + y², we get:</em>
= (a)² + (2b)² + 2 × (a) × (2b)
= a² + 4b² + 4ab
= a² + 4ab + 4b² Ans.
#2.
(5x - 3y)²
<em>Using identity (a - b)² = a² - 2ab + b², we get:</em>
= (5x)² + (3y)² - 2 × (5x) × (3y)
= 25x² + 9y² - 30xy
= 25x² - 30xy + 9y² Ans.
#3.
(3a + 4)(3a - 4)(9a² + 16)
<em>Using identity (x + y)(x - y) = x² - y², we get:</em>
= [(3a)² - (4)²][9a² + 16]
= (9a² - 16)(9a² + 16)
= (9a²)² - (16)²
= 81a⁴ - 256 Ans.
The linear equation that has a slope of -7 and crosses the x-axis at (3, 0) is:
y = -7x + 21
<h3>
How to find the linear equation?</h3>
A general linear equation is:
y = a*x +b
Where a is the slope and b is the y-intercept.
The slope must be equal to the limit found in part a, and you say that it is equal to -7, so the slope is -7. And for how is written the problem, I understand that it crosses the x-axis at x = 3.
Then we will have:
y = -7*x + b
Such that, when x = 3, y = 0, then:
0 = -7*3 + b
21 = b
Then the linear equation is y = -7x + 21
If you want to learn more about linear equations:
brainly.com/question/1884491
#SPJ1
6/9 (2/3) and 2/3. Hope this helps you.
