1). 6a+6b+a+b=7a+7b=7(a+b)
2). 4(x-y)+3(x-y)(x-y)=(x-y)(4+3(x-y))=(x-y)(4+3x-3y)<em />
1) (a+b)² - (a-b)² = 2b * 2a = 4ab
2) (m+4)² - 4 (m+1)² = m² + 8m + 16 - 4 (m² + 2m +1) = m² + 8m + 16 - 4m² - 8m - 4 = -3m + 12
3) 3(2-y)² + 4(y-5)² = 3(4-4y+y²) + 4(y² - 10y + 25) = 12 - 12y + 3y² + 4y² - 40y + 100 = 112 - 52y + 7y² = 7y² - 52y + 112
4) 5(3-5x)² - 5(3x-7) * (3x+7) = 5 ((3-5x)² - (3x-7) * (3x+7)) = 5 (9-30x + 25x² - (9x² - 49)) = 5 (9 - 30x + 25x² - 9x² + 49) = 5 (58 - 30x + 16x²) = 5 * 2 (29 - 15x + 8x²) = 10 (29 - 15x + 8x²)
5) (a+1)² + 3(a-1)² - 5 (a-1)* (a+1) = a² + 2a + 1 + 3 (a² - 2a + 1) - 5 (a² -1) = a² + 2a + 1 + 3a² - 6a + 3 - 5a² + 5 = -a² - 4a + 9
6) (x-1)² - 4(x+1)² - 6 (x+1) * (x-1) = x² - 2x + 1 - 4 (x² + 2x + 1) - 6 (x² -1) = x² - 2x + 1 - 4x² - 8x - 4 - 6x² + 6 = -9x² - 10x + 3.
1)sin 420° = sin(360° + 60°) = sin 60° = √3/2