а) (х+3у)² = х² + 6ху + 9у²(х+3у)(х-3у) = х² - 9у²(х+3у)² + (х+3у)(х-3у) = х² + 6ху + 9у² + х² - 9у² = 2х² + 6ху
б) (4х+5)² = 16х² + 40х + 25(4х-1)² = 16х² - 8х + 12(4х+5)(4х-1) = 2(16х² + 16х - 5х - 5) = 2(16х² + 11х - 5) = 32х² + 22х - 10
(4 х+5)² + (4 х-1)² - 2(4 х+5)(4 х-1) = (16х² + 40х + 25) + (16х² - 8х + 1) - (32х² + 22х - 10) = 16х² + 40х + 25 + 16х² - 8х + 1 - 32х² - 22х + 10 == 16х² + 16х² - 32х² + 40х - 8х - 22х + 25 + 1 - 10 = 0 + 10х + 16 = 10х + 16.
а) (х+3у)² = х² + 6ху + 9у²
(х+3у)(х-3у) = х² - 9у²
(х+3у)² + (х+3у)(х-3у) = х² + 6ху + 9у² + х² - 9у² = 2х² + 6ху
б) (4х+5)² = 16х² + 40х + 25
(4х-1)² = 16х² - 8х + 1
2(4х+5)(4х-1) = 2(16х² + 16х - 5х - 5) = 2(16х² + 11х - 5) = 32х² + 22х - 10
(4 х+5)² + (4 х-1)² - 2(4 х+5)(4 х-1) = (16х² + 40х + 25) + (16х² - 8х + 1) - (32х² + 22х - 10) = 16х² + 40х + 25 + 16х² - 8х + 1 - 32х² - 22х + 10 =
= 16х² + 16х² - 32х² + 40х - 8х - 22х + 25 + 1 - 10 = 0 + 10х + 16 = 10х + 16.