Question

1) (x-2)(x+3)+(x+2)(x-3) 2) (a-1)(a+2)+(a+1)(a-2) 3) (a+1)(a+2)+(a+3)(a+4) 4) (x-1)(x-2)+(x-3)(x-4) 5)(4b^2+2a^2-4ab)(ab+2a^2-3b^3) 6)(5ab-3a^2-2b^2)(-4b^2-ab-6a^2) 7)(7+3a^2-3a)(5-2a-a^2) 8)(5xy^2-3x^3+2x^2y)(2x^2-xy-4y^2)

Answer 1

Преобразуй выражение в дробь и, если возможно, сократи ее, если значения всех переменных отличны от нуля: 1) m/3 – 3/m; 2) 2a + b/5; 3) x^2/9 * 6/xy; 4) (5c) : c^2/d.

Answer 2

Let's simplify each of the given expressions:

1. (x-2)(x+3)+(x+2)(x-3) Expanding each term: (xx + x3 - 2x - 22) + (xx + x(-3) + 2x - 23) Combining like terms: x^2 + 3x - 2x - 4 + x^2 - 3x + 2x - 6 Simplifying: 2x^2 - 8

2. (a-1)(a+2)+(a+1)(a-2) Expanding each term: (aa + a2 - 1a - 12) + (aa + a(-2) + 1a - 12) Combining like terms: a^2 + 2a - a - 2 + a^2 - 2a + a - 2 Simplifying: 2a^2 - 6

3. (a+1)(a+2)+(a+3)(a+4) Expanding each term: (aa + a2 + 1a + 12) + (aa + a4 + 3a + 34) Combining like terms: a^2 + 2a + a + 2 + a^2 + 4a + 3a + 12 Simplifying: 2a^2 + 10a + 14

4. (x-1)(x-2)+(x-3)(x-4) Expanding each term: (xx + x(-2) - 1x - 1(-2)) + (xx + x(-4) - 3x - 3(-4)) Combining like terms: x^2 - 2x - x + 2 + x^2 - 4x - 3x + 12 Simplifying: 2x^2 - 10x + 14

5. (4b^2 + 2a^2 - 4ab)(ab + 2a^2 - 3b^3) Expanding each term: (4b^2 * ab + 4b^2 * 2a^2 + 4b^2 * (-3b^3)) + (2a^2 * ab + 2a^2 * 2a^2 + 2a^2 * (-3b^3)) + (-4ab * ab + -4ab * 2a^2 + -4ab * (-3b^3)) Simplifying: 4ab^3 + 8a^2b^2 - 12b^5 + 2a^3b + 4a^4 - 6a^2b^3 - 4a^2b - 8a^3b^3 + 12ab^4

6. (5ab - 3a^2 - 2b^2)(-4b^2 - ab - 6a^2) Expanding each term: (5ab * -4b^2 + 5ab * (-ab) + 5ab * (-6a^2)) + (-3a^2 * -4b^2 + -3a^2 * (-ab) + -3a^2 * (-6a^2)) + (-2b^2 * -4b^2 + -2b^2 * (-ab) + -2b^2 * (-6a^2)) Simpl