Question

21, 1) (2x - 3)²-(3x - 5)²; 3) 16(2x + 5)² - 81(4 - 5x)²; 5) (2a - 1)³ - 27a³; 2) (3x + 2)²-(1-2x)²; 4) 0,01a²- (a − 3)²; 6) (3x - 2)³ + (5 - 4x)³.​.

Answer 1

$1)$

${(2x - 3)}^{2} - {(3x - 5)}^{2} = {4x}^{2} - 12x + 9 - {9x}^{2} + 30x - 25 = - {5x}^{2} + 18x - 16$

$3)$

$16 {(2x + 5)}^{2} - 81 {(4 - 5x)}^{2} = 16( {4x}^{2} + 20x + 25) - 81(8 - 40x + {25x}^{2} ) = {64x}^{2} + 320x + 400 - 648 + 3240x - {2025x}^{2} = - {1961x}^{2} + 3560x - 248$

$5)$

${(2a - 1)}^{3} - {27a}^{3} = {8a}^{3} - 12 {a}^{2} + 6a - 1 - 27 {a}^{3} = - {19a}^{3} - {12a}^{2} + 6a - 1$

$2)$

${(3x + 2)}^{2} - {(1 - 2x)}^{2} = {9x}^{2} + 12x + 4 - 1 + 4x - {4x}^{2} = {5x}^{2} + 16x + 3$

$4)$

$0. {01a}^{2} - {(a - 3})^{2} = {0.01a}^{2} - {a}^{2} + 6a - 9 = - 0.99 {a}^{2} + 6a - 9$

$6)$

${(3x - 2)}^{3} + {(5 - 4x)}^{3} = 27 {x}^{3} - {54x}^{2} + 36x - 8 + 125 - 300x + {240x}^{2} - {64x}^{3} = - {37 x }^{3} + {186x}^{2} - 264x + 117$