Question

Упростить: (2x+5)² - 2(2x+5)(x-3)+(x-3)²

Answer 1

$(2x+5)^2-2\cdot (2x+5)\cdot (x-3)+(x-3)^2=\\\\=\Big ((2x+5)-(x-3)\Big )^2=\Big (x+8\Big )^2=x^2+16x+64$

Answer 2

To simplify the expression (2x+5)² - 2(2x+5)(x-3) + (x-3)², follow these steps:

Step 1: Expand each squared term: (2x+5)² = (2x+5)(2x+5) = 4x² + 20x + 25 (x-3)² = (x-3)(x-3) = x² - 6x + 9

Step 2: Expand the product of two binomials: 2(2x+5)(x-3) = 2(2x)(x) + 2(2x)(-3) + 2(5)(x) + 2(5)(-3) = 4x² - 12x + 10x - 30 = 4x² - 2x - 30

Step 3: Now, rewrite the entire expression with the expanded terms: (2x+5)² - 2(2x+5)(x-3) + (x-3)² = (4x² + 20x + 25) - (4x² - 2x - 30) + (x² - 6x + 9)

Step 4: Simplify the expression by combining like terms: = 4x² + 20x + 25 - 4x² + 2x + 30 + x² - 6x + 9 = 4x² - 4x² + x² + 20x + 2x - 6x + 25 + 30 + 9 = x² + 16x + 64

The simplified expression is x² + 16x + 64.