Question

Completați:
a) a - b =( ....... ) ( ....... );
b) a² + 2ab + b2 = .........;
c) a² - 2ab + b2 = ........
Descompuneți în factori:
a) 4x² - 49;
b) 25–9x?;
c) x4 -81;
d) (x-1)- 16;
e) 9-(x+2)";
f) 9x? - (2x – 3)”;
g) (2x-3y) – 4y?; h) 16x°-(3x – y)?;
1) 100x² – 4(3x+1)?; j) (2x+5)? -(x-1);
k) (3x–5)²-(2x+3)”; 1) 4(2x+5)? -(x+3)”;
m) 25(x+1)? -9(x-2).
Algebră . 87​

Answer 1

Răspuns:

Completați:

a) a²-b²=(a-b)(a+b);

b) a²+2ab+b²=(a+b)²;

c) a²-2ab+b²=(a+b)².

Descompuneți în factori:

a) 4x²-49=(2x-7)(2x+7);

b) 25-9x=(5-3x)(5+3x);

c) x⁴-81=(x²-9)(x²+9)=(x-3)(x+2)(x²+9);

d) (x-1)²-16=(x-1-16)(x-1+16)=(x-17)(x+15);

e) 9-(x+2)²=(3-x-2)(3+x+2)=(1-x)(5+x);

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

g) (2x-3y)²-4y²=(2x-3y-2y)(2x-3y+2y)=(2x-5y)(2x-y);

h) 16x²-(3x-y)²=(4x-3x+y)(4x+3x-y)=(x+y)(7x-y);

i) 100x²–4(3x+1)²=[10x-2(3x+1)][10x+2(3x+1)]=(10v-6v-2)(10x+6x+2)=(4x-2)(16x+2)=4(2x-1)(8x+1);

j) (2x+5)²-(x-1)²=(2x+5-x+1)(2x+5+x-1)=(x+6)(3x+4);

k) (3x–5)²-(2x+3)²=(3x-5-2x-3)(3x-5+2x+3)=(x-8)(5x-2);

l) 4(2x+5)²-(x+3)²=[2(2x+5)-x-3][2(5x+5)+x+3]=(4x+10-x-3)(4x+10+x+3)=(5x+7)(5x+13);

m) 25(x+1)²-9(x-2)²=[5(x+1)-3(x-2)][5(x+1)+3(x-2)]=(5x+5-3x+6)(5x+5+3x-6)=(2x+11)(8x-1).

Explicație pas cu pas: