Question

ajutatima va rog frumos

Answer 1

$1a).(2a^2-3a+1)-(7a^2-5a)=2a^2-3a+1-7a^2+5a= \\ =-5a^2+2a+1 \\ \\ b).3x(4x^2-x)=12x^3-3x^2 \\ \\ c).(a-5)(a-3)=a^2-3a-5a+15=a^2-8a+15 \\ \\ d).(5x+4)(2x-1)=10x^2-5x-4+8x=10x^2+3x-4 \\ \\ e).(b-2)(b^2+2b-3)=b^3+2b^2-3b-2b^2-4b+6=b^3-7b+6$

$2a).(x+6)^2=x^2+2 \cdot x \cdot 6+6^2=x^2+12x+36 \\ \\ b).(3a-1)^2=(3a)^2-2 \cdot 3a \cdot 1+1^2=9a^2-6a+1 \\ \\ c).(3y-2)(3y+2)=9y^2-4 \\ \\ d).(4x+3y)(4x-3y)=16x^2-9y^2$

$3a).(b-8)^2-(64-6b)=b^2-2 \cdot b \cdot 8+8^2-64+6b= \\ =b^2-16b+64-64+6b=b^2-10b \\ \\ b).(x+y)(x-y)-(x^2+3y^2)=x^2-y^2-x^2-3y^2=-4y^2 \\ \\ c).2a(a+1)-(a-2)(a+4)=2a^2+2a-(a^2+4a-2a-8)= \\ =2a^2+2a-a^2-4a+2a+8=a^2+8 \\ \\ d).(y+2)^2-2y(y+2)=y^2+2 \cdot y \cdot 2+2^2-2y^2-4y= \\ =y^2+4y+4-2y^2-4y=-y^2+4$

$4a).3x^2+9xy=3x(x+3y) \\ \\ b).2a-2b+ca-cb=2(a-b)+c(a-b)=(a-b)(2+c) \\ \\ c).25-y^2=(5-y)(5+y) \\ \\ d).a^2-6ab+9b^2=a^2-3ab-3ab+9b^2=a(a-3b)-3b(a-3b)= \\ =(a-3b)(a-3b)=(a-3b)^2$