Question by Kaya Renger - Discuss with MathYouLike

Kaya Renger Coordinator

16/09/2017 at 21:31

a) a² + 2(a + 1)² + 3(a + 2)² + 4(a + 3)² = (a + 5)² + (3a + 5)²

b) (a + b)(a - b) + (b + c)(b - c) = (a + c)(a - c)

c) (ax + by)² + (ay - bx)² = (a² + b²)(x² + y²)

List of answers

Phan Thanh Tinh Coordinator 16/09/2017 at 22:48

a) a² + 2(a + 1)² + 3(a + 2)² + 4(a + 3)²

= a² + 2(a² + 2a + 1) + 3(a² + 4a + 4) + 4(a² + 6a + 9)

= a² + 2a² + 4a + 2 + 3a² + 12a + 12 + 4a² + 24a + 36

= 10a² + 40a + 50 = a² + 10a + 25 + 9a² + 30a + 25

= (a + 5)² + (3a + 5)²

b) (a + b)(a - b) + (b + c)(b - c) = a² - b² + b² - c²

= a² - c² = (a + c)(a - c)

c) (ax + by)² + (ay - bx)²

= a²x² + 2axby + b²y² + a²y² - 2axby + b²x²

= a²x² + a²y² + b²x² + b²y²

= a²(x² + y²) + b²(x² + y²) = (a² + b²)(x² + y²)
Selected by MathYouLike
Vũ Trung Dũng 27/09/2017 at 18:48

a) a2 + 2(a + 1)2 + 3(a + 2)2 + 4(a + 3)2

= a2 + 2(a2 + 2a + 1) + 3(a2 + 4a + 4) + 4(a2 + 6a + 9)

= a2 + 2a2 + 4a + 2 + 3a2 + 12a + 12 + 4a2 + 24a + 36

= 10a2 + 40a + 50 = a2 + 10a + 25 + 9a2 + 30a + 25

= (a + 5)2 + (3a + 5)2

b) (a + b)(a - b) + (b + c)(b - c) = a2 - b2 + b2 - c2

= a2 - c2 = (a + c)(a - c)

c) (ax + by)2 + (ay - bx)2

= a2x2 + 2axby + b2y2 + a2y2 - 2axby + b2x2

= a2x2 + a2y2 + b2x2 + b2y2

= a2(x2 + y2) + b2(x2 + y2) = (a2 + b2)(x2 + y2)

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