Question

prosze o zadania 13 14 oraz 11 i 12

Answer 1

12.

a)

ac+bc+a(a+b)=c(a+b)+a(a+b)=(a+b)(c+a)

b)

a(b+c)-b-c=a(b+c)-(b+c)=(b+c)(a-1)

c)

m(3a-b)-3a+b=m(3a-b)-(3a-b)=(3a-b)(m-1)

d)

a(x-y)-bx+by=a(x-y)-b(x-y)=(x-y)(a-b)

 

11.

a) 2x⁴-2=2(x⁴-1)=2(x²-1)(x²+1)=2(x-1)(x+1)(x²+1)

b) 4a⁴-64b⁴=4(a⁴-16b⁴)=4(a²-4b²)(a²+4b²)=4(a-2b)(a+2b)(a²+4b²)

c) 125a²b²c⁴ - 45x⁴y²c⁴=5c⁴(25a²b²-9x⁴y²)=5c⁴(5ab-3x²y)(5ab+3x²y)

d) 162x⁴y-62y⁵=2y(81x⁴-16y⁴)=2y(9x²-4y²)(9x²+4y²)=2y(3x-2y)(3x+2y)(9x²+4y²)

e) a⁷-a³=a³(a⁴-1)=a³(a²-1)(a²+1)=a³(a-1)(a+1)(a²+1)

f) 8y²-8x⁸y²=8y²(1-x⁸)=8y²(1-x⁴)(1+x⁴)=8y²(1-x²)(1+x²)(1+x⁴)=8y²(1-x)(1+x)(1+x²)(1+x⁴)

 

zadania 13 i 14  w załączniku