Question

Descompuneti :

1. (x+3)^{2}-4
2. (x-3)^{2}-25
3. (x+2)^{2}-16
4. (x-5)^{2}-81
5. (x+5)^{2}-4x^{2}
6. (x-7)^{2}-9x^{2}
7. 4(x-1)^{2}-9
9. 9(x-2)^{2}-25x^{2}

Answer 1

1)

(x+3)²-4=

(x+3)²-2²=

(x+3+2)(x+3-2)=

(x+5)(x+1)

2)

(x-3)²-25=

(x-3)²-5²=

(x-3+5)(x-3-5)=

(x+2)(x-8)

3)

(x+2)²-16=

(x+2)²-4²=

(x+2+4)(x+2-4)=

(x+6)(x-2)

4)

(x-5)²-81=

(x-5)²-9²=

(x-5+9)(x-5-9)=

(x+4)(x-14)

5)

(x+5)²-4x²=

(x+5)²-2²x²=

(x+5)²-(2x)²=

(x+5-2x)(x+5+2x)=

(-x+5)(3x+5)

6)

(x-7)²-9x²=

(x-7)²-3²x²=

(x-7)²-(3x)²=

(x-7-3x)(x-7+3x)=

(-2x-7)(4x-7)

7)

4(x-1)²-9=

2²(x-1)²-3²=

(2(x-1))²-3²=

(2(x-1)-3)(2(x-1)+3)=

(2x-2-3)(2x-2+3)=

(2x-5)(2x+1)

8)

9(x-2)²-25x²=

3²(x-2)²-5²x²=

(3(x-2))²-(5x)²=

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

(3x-6-5x)(3x-6+5x)=

(-2x-6)(8x-6)=

(-2(x+3))•2(4x-3)=

-2•2(x+3)(4x-3)=

-4(x+3)(4x-3)