Question

Представьте в виде произведения : 1 ) 9x^2 - 4y^2 - 3x + 2y 2 ) 81 - ( 3 - 8y )^2 3 ) 36 - ( y + 1 )^2 4 ) ( 4 - 5x )^2 - 64 . !

Answer 1

1 ) 9x^2 - 4y^2 - 3x + 2y=(3х-2у)(3х+2у)-(3х-2у)=(3х-2у)(2х+2у-1)
2 ) 81 - ( 3 - 8y )^2=(9-3+8у)(9+3-8у)=(6+8у)(12-8у)=8(3+4у)(3-2у)
3 ) 36 - ( y + 1 )^2=(6-у-1)(6+у+1)=(5-у)(7+у)
4 ) ( 4 - 5x )^2 - 64 =(4-5х-8)(4+5х+8)=-(4+5х)(12+5х)
Формула сокращенного умножения
(а-в)(а+в)=а^2-в^2

Answer 2

Объяснение:

Воспользуемся формулой сокращенного умножения :

$a^{2} -b^{2} = (a-b)(a+b)$, а в первом примере воспользуемся группировки.

$1) 9x^{2} -4y^{2} - 3x+2y= (3x-2y)( 3x+2y) - ( 3x-2y)=\\= ( 3x-2y) ( 3x+2y-1);\\2) 81- (3-8y) ^{2} = 9^{2} - (3-8y) ^{2} = = ( 9-3+8y)( 9+3-8y) = (6+8y)(12-8y) = \\=2( 3+4y) * 4( 3-2y)= 8(3+4y) (3-2y);\\3) 36- (y+1) ^{2} = 6^{2} - (y+1) ^{2} =( 6-y-1)(6+y+1) = (5-y)(7+y);\\4) (4-5x) ^{2} -64= (4-5x) ^{2} -8^{2}=(4-5x-8)( 4-5x+8)= (-4-5x) (12-5x)=\\= -(4+5x)( 12-5x) = (5x+4)( 5x-12).$

Answer 3

Применим формулу сокращённого умножения:

a² - b² = (a - b)·(a + b).

1) 9·x²-4·y²-3·x+2·y = (3·x)²-(2·y)²-(3·x-2·y) = (3·x-2·y)·(3·x+2·y) - (3·x-2·y) =

= (3·x-2·y)·(3·x+2·y-1);

2) 81 - (3-8·y)²  = 9² - (3-8·y)²  = (9-(3-8·y))·(9+(3-8·y)) = (9-3+8·y)·(9+3-8·y) =

= (6+8·y)·(12-8·y) = 2·(3+4·y)·4·(3-2·y) = 8·(3+4·y)·(3-2·y);

3) 36-(y+1)² = 6²-(y+1)² = (6-(y+1))·(6+(y+1)) = (6-y-1)·(6+y+1) = (5-y)·(7+y);

4) (4-5·x)²-64 = (4-5·x)²-8² = (4-5·x-8)·(4-5·x+8) = (-4-5·x)·(12-5·x) =

= -(4+5·x)·(12-5·x) = (4+5·x)·(5·x-12).