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= x² + 4x + 2x + 8
= x² + 6x + 8
b. (2p + 5)(2p - 5)
= 4p² - 10p + 10p - 25
= 4p² - 25
c. (4 + 2m)(m - 8)
= 4m - 32 + 2m² - 16m
= 2m² - 12m - 32
d. (10x - 3)(2x - 1)
= 20x² - 10x - 6x + 3
= 20x² - 16x + 3
e. (7 - x)(7x - 1)
= 49x - 7 - 7x² + x
= -7x² + 50x - 7
7. L = 1/2 × a × t
L = 1/2 × (5x + 3) × (2x - 2)
L = 1/2 × (5x + 3) × 2(x - 1)
L = (5x + 3)(x - 1)
L = 5x² - 5x + 3x - 3
L = 5x² - 2x - 3
8a. 5p²q : pq
= pq(5p)/pq
= 5p
b. 2ab² : 6a²b
= 2ab(b)/2ab(3a)
= b/(3a)
c. (8xy² + 2x) : 4y
= 2(4xy² + x)/(4y)
= (4xy² + x)/(2y)
d. (5m² - 5n²) : (m² - n²)
= 5(m² - n²)/(m² - n²)
= 5
e. (24ab + 6b) : (12ab² - 6a)
= 6(4ab + b)/6(2ab² - a)
= (4ab + b)/(2ab² - a)
9a. (2x + 5)³
= (2x)³ + 3 . (2x)² . 5 + 3 . 2x . 5² + 5³
= 8x³ + 60x² + 150x + 125
b. (-x + 8)²
= (-x)² + 2 . (-x) . 8 + 8²
= x² - 16x + 64
c. (2x - 2y)²
= (2x)² - 2 . 2x . 2y + (2y)²
= 4x² - 8xy + 4y²
10a. (x + 4)² + (x - 4)²
= (x² + 8x + 16) + (x² - 8x + 16)
= 2x² + 32
b. (5 - y)² + (5y - 1)²
= (25 - 10y + y²) + (25y² - 10y + 1)
= 26y² - 20y + 26
c. (1/2x + 2)² + (1/2x - 2)²
= (1/4x² + 2x + 4) + (1/4x² - 2x + 4)
= 1/2x² + 8