Directions: State whether each expression is a differences of two squares. If yes, factor the binomials completely. If not write Bluff.
1. y² - 100
2.a² - 49
3.a²b² - 64
4.y³ - 25
5. b² - 1
6.c² + 4
7.(p + q)² - 81
8.a² - (c - d)²
9.m² n² - 9x⁴
10.x² y⁸ - 36z¹⁰
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Answer:
Step-by-step explanation:
Difference of two squares
x² - y² = (x+y)(x-y)
[tex] \:[/tex]
a²b² - 64
a²b² = (ab)²
- 64 = 8(-8)
∴a²b² - 64 = (ab-8)(ab+8)
[tex] \:[/tex]
(p+q)² - 81
- 81 = 9(-9)
∴(p+q)² - 81 = (p+q+9)(p+q-9)
[tex] \:[/tex]
a² - (c-d)²
a² = (a)²
- (c-d)² = (c-d)(-1×c-d) = (c-d)(d-c)
∴a² - (c-d)² = (a+c-d)(a-c+d)
[tex] \:[/tex]
m² n² - 9x⁴
m²n² = (mn)²
- 9x⁴ = (3x)(-3x)
∴m² n² - 9x⁴ = (mn+3x²)(mn-3x²)
[tex] \:[/tex]
x² y⁸ - 36z¹⁰
x²y⁸ = (xy⁴)²
- 36z¹⁰ = (6z⁵)(-6z⁵)
∴x² y⁸ - 36z¹⁰ = (xy⁴ + 6z⁵)(xy⁴ - 6z⁵)
[tex] \:[/tex]
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