Answers for each part (1) 2y^2+4y−9
(2) 18x^5y^4z
(3) 6x^5−12x^ 4+9x^3
(4) The Coefficient for second term is 24
(5) x^3−7x^2+4x+30
The Simplifications can be done as follows
(1) There are two given simple polynomial expressions which are given for simplification. On subtracting the second expression from the first expression we get
[tex]y^2 -3y -5 -( -y^2-7y +4) = y^2 -3y -5 + y^2 +7y-4 \\= 2y^2 +4y -9[/tex]
(2)
This is question of multiplication of polynomial expressions which can be done as follows
[tex](6xy^3 z)\times (3x^2y\times x^2)[/tex]
[tex]= 18x^5 y^4 z[/tex]
(3) This is question of multiplication of polynomial expressions which can be done as follows
−3x3(−2x2+4x−3)
[tex]-3x^3( -2x^2+4x-3)[/tex]
[tex]= 6x^5 -12x^4 +9x^3[/tex]
(4)
The polynomial expression with three terms is called as trinomial expression. On expansion of the given expression according to the formula of [tex]\rm (a+b)^2 = a^2 +2ab+b^2[/tex] we get
[tex](6P + 2)^2 = 36P^2 + 4 + 2\times 6P\times 2 \\= 36P^2 + 24P+ 4[/tex]
The coefficient of second term of the trinomial = 24
(5) [tex](x-5) ( x^3-2x-6)[/tex]
This is a problem of polynomial expression multiplication
According to the identity
[tex]\rm (a+b) (c+d) = ac + ad +bc +bd[/tex]
On expansion we get the expression
[tex]x^3 -2x^2 -6x -5x^2+10x+30[/tex]
[tex]= x^3 -7x +4x +30[/tex]
For more information please refer to the link below
https://brainly.com/question/11536910
