Respuesta :
[tex]9x^4+102x^3+253x^2-204x+36[/tex] is the result of multiplying (3x-1) to the second power and (x+6) to the second power
Solution:
Given that we have to find the result of multiplying polynomials (3x-1) to the second power and (x+6) to the second power
"Second power" means the term is raised to power of 2
Therefore,
We have to multiply [tex](3x-1)^2 \text{ and }(x+6)^2[/tex]
[tex]\rightarrow (3x-1)^2 \times (x+6)^2[/tex]
We can use the algebraic identity to expand the above expression
[tex](a+b)^2 = a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2[/tex]
Applying these in above expression, we get
[tex]\rightarrow ((3x)^2-2(3x)(1)+1^2) \times (x^2+2(x)(6)+6^2)\\\\\rightarrow (9x^2-6x+1) \times (x^2+12x+36)[/tex]
Multiply each term in first bracket with each term in second bracket
[tex]\rightarrow 9x^2(x^2)+(9x^2)(12x)+(9x^2)(36)-6x(x^2)-6x(12x)-6x(36) + x^2+12x+36[/tex]
Simplify the above expression
[tex]\rightarrow 9x^4+108x^3+324x^2-6x^3-72x^2-216x+x^2+12x+36[/tex]
Combine the like terms
[tex]\rightarrow 9x^4+102x^3+253x^2-204x+36[/tex]
Thus the above expression is the result of multiplying (3x-1) to the second power and (x+6) to the second power
