262,263,265,267,268

283.284.285.288

283

Ա) ax+bx = x(a+b)

Բ) am-ank = a(m-nk)

Գ) x²y+xy² = xy(x+y)

Դ) p²q³-p³q = p²q(q²-p)

Ե) a²bc+ab²c+abc² = abc(a+b+c)

284

Ա) -1/2m³+2m²-m = m(-1/2m²+3m-1)

Բ) 1/3pq²+1/6pq-p²q = pq(1/3q+1/6-p)

Գ) 1/3x²y³+1/4x³y²+1/12x³y³ = x²y²(1/3y+1/4x+1/12xy)

Դ) 0,2a⁵b³-1,2a³b⁴+0,7ab³ = ab³(0,2a⁴-1,2a²b+0,7)

285

Ա) 16a²bc³-12ac³+28b²c²-8abc⁵ = 4c²(4a²bc-3ac+7b²-2abc³)

Բ) 12x²yz+18xy³z²-27x⁵z⁶-24xy⁴z⁴ = 3xz(4xy+6y³z-9x⁴z⁵-8y⁴z³)

Գ) 0,25m²n²k-0,45m³nk²-1,5mn³k²-0,05m⁵n³k = 5mnk(00,5mn-0,09m²k-0,3n²k-0,01m⁴n²)

Դ) 1,42x²y⁴z³-21/2xy³z²-0,2x³y²z+31/3xy³z² = xy²z(1,42xy²z²-21/2yz-0,2x²+31/3y)

288

Ա) (a+b)a+(a+b)c = (a+b)(a+c)

Բ) (a+b)x-(a+b)y = (a+b)(x-y)

Գ) 2(a+b)+(a+b)x = (a+b)(2+x)

Դ) x(a+b)-2(a+b) = (a+b)(x-2)

Ե) 2x(a+b)+(a+b) = (a+b)(2x+1)

Զ) (a+b)3x-2y(a+b) = (a+b)(3x-2y)

270.272

270

Ա) a³+b³+3ab(a+b) = (a+b)³

a³+b³+3ab(a+b) = a³+b³+3a²b+3ab² = (a+b)³

Բ) a³-3ab(a-b)-b³ = (a-b)³

a³-3ab(a-b)-b³ = a³-3a²b+3ab²-b³ = (a-b)³

272

Ա) (m²+1)(n²+1) = (mn-1)²+(n+m)²

(m²+1)(n²+1) = m²n²+m²+n²+1

(mn-1)²+(n+m)² = m²n²-2mn+1+n²+2mn+m² = m²n²+m²+n²+1

Բ) (a²+b²)(c²+d²) = (ac-bd)²+(bc+ad)²

(a²+b²)(c²+d²) = a²c²+a²d²+b²c²+b²d²

(ac-bd)²+(bc+ad)² = a²c²-2acbd+b²d²+b²c²+2bcad+a²d² = a²c²+b²d²+b²c²+a²d²