The expanded expressions are shown below:
- (x + 1)² = x² + 2 · x + 1
- (x - 3)² = x² - 6 · x + 9
- (x + 4)² = x² + 8 · x + 16
- (x - 1/2)² = x² - x + 1/4
- 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75
- (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2
How to expand perfect square trinomials
Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:
a) (x + 1)² = x² + 2 · x + 1
b) (x - 3)² = x² - 6 · x + 9
c) (x + 4)² = x² + 8 · x + 16
d) (x - 1/2)² = x² - x + 1/4
e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75
f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2
To learn more on perfect square trinomials: https://brainly.com/question/385286
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