Question

Scrieți sub formă de produs:
(x+3)²-1;
64-(b+1)²;
(4a-3)²-16;
25-(a+7)²;
(5y-6)²-81;
1-(2x-1)²;
9y²-(1+2y)²;
(3a-5)²-16a²;
49x²-(y+8x)²;
(5a-b)²-25a²;
(-2a²+3b)²-4a²;
(15-4b²)²-16b⁴.​

Answer 1

Explicație pas cu pas:

$(x+3)^{2} -1 = (x + 3 - 1)(x + 3 + 1) = (x + 2)(x + 4)$

$64-(b+1)^{2} = {8}^{2} - (b+1)^{2} = (8 - b - 1)(8 + b + 1) = (7 - b)(9 + b)$

$(4a-3)^{2} -16 = (4a-3)^{2} - {4}^{2} = (4a - 3 - 4)(4a - 3 + 4) = (4a - 7)(4a + 1)$

$25-(a+7)^{2} = {5}^{2} - (a+7)^{2} = (5 - a - 7)(5 + a + 7) = (- 2 - a)(12 + a) = - (2 + a)(12 + a)$

$(5y-6)^{2} - 81 = (5y-6)^{2} - {9}^{2} = (5y - 6 - 9)(5y - 6 + 9) =(5y - 15)(5y + 3) = 5(y - 3)(5y + 3)$

$1 - (2x-1)^{2} = (1 - 2x + 1)(1 + 2x - 1) = (2 - 2x)(2x) = 4x(1 - x)$

$9y^{2} - (1+2y)^{2} = (3y)^{2} - (1+2y)^{2} = (3y - 1 - 2y)(3y + 1 + 2y) = (y - 1)(5y + 1)$

$(3a-5)^{2} - 16a^{2} = (3a-5)^{2} - (4a)^{2} = (3a - 5 - 4a)(3a - 5 + 4a) = ( - a - 5)(7a - 5) = - (a + 5)(7a - 5)$

$49x^{2} - (y+8x)^{2} = (7x)^{2} - (y+8x)^{2} = (7x - y - 8x)(7x + y + 8x) = ( - x - y)(15x + y) = - (x + y)(15x + y)$

$(5a-b)^{2} -25a^{2} = (5a - b) - (5a)^{2} = (5a - b - 5a)(5a - b + 5a) = ( - b)(10a - b) = - b(10a - b)$

$(-2a^{2} +3b)^{2} - 4a^{2} = (-2a^{2} +3b)^{2} - (2a)^{2} = (- 2a^{2} + 3b - 2a)(- 2a^{2} + 3b + 2a)$

$(15 - 4b^{2})^{2} -16b^{4} = (15 - 4b^{2})^{2} - (2b)^{4} = (15 - 4b^{2} - 2b)(15 - 4b^{2} + 2b)$