Question

Упростить выражение 1). 7(x+8) + (x+8)(x-8) 2). (x-3)(3+x)+(x-3)² 3). (y-5)²-(y+7)² 4). (x+3)(x-3) - x² + 2x​

Answer 1

$\displaystyle\bf\\1)\\\\7(x+8)+(x+8)(x-8)=7x+56+x^{2} -64=x^{2} +7x-8\\\\\\2)\\\\(x-3)(3+x)+(x-3)^{2} =x^{2} -9+x^{2} -6x+9=2x^{2} -6x\\\\\\3)\\\\(y-5)^{2} -(y+7)^{2} =y^{2} -10y+25-(y^{2}+14y+49)=\\\\=y^{2} -10y+25-y^{2} -14y-49=-24y-24\\\\\\4)\\\\(x+3)(x-3)-x^{2} +2x=x^{2} -9-x^{2} +2x=2x-9$

Answer 2

Упростить выражение

1) 7(x+8) + (x+8)(x-8) 2) (x-3)(3+x) + (x-3)² 3) (y-5)² - (y+7)² 4) (x+3)(x-3) - x² + 2x

1) 7(x+8) + (x+8)(x-8)

To simplify the expression, we can start by distributing and combining like terms:

7(x+8) + (x+8)(x-8) = 7x + 56 + x(x-8) + 8(x-8) = 7x + 56 + x² - 8x + 8x - 64 = 7x + 56 + x² - 64 = x² + 7x - 8

So, the simplified expression is x² + 7x - 8.

2) (x-3)(3+x) + (x-3)²

Similarly, we can simplify this expression by distributing and combining like terms:

(x-3)(3+x) + (x-3)² = (x-3)(x+3) + (x-3)² = x(x-3) + 3(x-3) + (x-3)² = x² - 3x + 3x - 9 + x² - 6x + 9 = 2x² - 6x

The simplified expression is 2x² - 6x.

3) (y-5)² - (y+7)²

To simplify this expression, we can apply the difference of squares formula:

(y-5)² - (y+7)² = (y-5 + y+7)(y-5 - y-7) = (2y + 2)(-12) = -24y - 24

The simplified expression is -24y - 24.

4) (x+3)(x-3) - x² + 2x

We can simplify this expression by multiplying and combining like terms:

(x+3)(x-3) - x² + 2x = x² - 3x + 3x - 9 - x² + 2x = 5x - 9

The simplified expression is 5x - 9.

So, the simplified expressions for the given expressions are: 1) x² + 7x - 8 2) 2x² - 6x 3) -24y - 24 4) 5x - 9.