Question

1. (x-5)^2-(x-4)(x+4)+(x+1)^2. 2.(3x-2)^2-5(x-3)(x+3)-(2x+3)^2 ​

Answer 1

1. x^2-10x+25-(x^2-16)+x^2+2x+1 = 2x^2-8x+26-x^2+16= x^2-8x+42

2. 9x^2-12x+4-5(x^2-9)-4x^2-12x-9= 5x^2-24x-5-5x^2+45= -24x+40

Answer 2

Răspuns:

x²-8x+42

-24x+40

Explicație pas cu pas:

1.(x-5)²-(x-4)(x+4)+(x+1)²

folosind formula (a-b)²=a²-2ab+b²,descompunem expresia (x-5)²

x²-10x+25

folosind formula (a-b)(a+b)=a²-b²,descompunem expresia (x-4)(x+4)

-(x²-16)

folosind formula (a+b)²=a²+2ab+b²,transformăm expresia (x+1)²

x²+2x+1

deci ne rămâne...

x²-10x+25-(x²-16)+x²+2x+1=x²-10x+25-x²+16+x²+2x+1

Avem x²-x²=0

-10x+2x=-8x

si

25+16+1=42

deci ne rămâne...

-8x+42+x²=x²-8x+42

2.(3x-2)²-5(x-3)(x+3)-(2x+3)²

folosind formula (a-b)²=a²-2ab+b²,transformam expresia (3x-2)²

9x²-12x+4

folosind formula (a-b)(a+b)=a²-b²,restrângem produsul (x-3)(x+3)

5(x²-9)

folosind formula (a+b)²=a²+2ab+b²,transformăm expresia (2x+3)²

deci ne rămâne...

9x²-12x+4-5(x²-9)-(4x²+12x+9)=9x²-12x+4-5x²+45-4x²-12x-9

Avem 9x²-5x²-4x²=0

-12x-12x=-24x

si

4+45-9=40

deci ne rămâne...

0-24x+40=-24x+40

Spor la treaba !