Answer:
The given multiplied expression is
[tex](7x^2+a^2)(x^2-3a^2)=7x^4-20x^2a^2-3a^4[/tex]
Step-by-step explanation:
Given expression is [tex](7x^2+a^2)(x^2-3a^2)[/tex]
To find the multiplication of the given expression :
[tex](7x^2+a^2)(x^2-3a^2)[/tex]
By using the distributive property to solve the given expression as below
[tex](7x^2+a^2)(x^2-3a^2)=(7x^2)(x^2)+(7x^2)(-3a^2)+(a^2)(x^2)+(a^2)(-3a^2)[/tex]
[tex]=7x^2.x^2-21x^2a^2+a^2x^2-3a^2.a^2[/tex]
[tex]=7x^{2+2}-21x^2a^2+a^2x^2-3a^{2+2}[/tex] ( by using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=7x^4-21x^2a^2+a^2x^2-3a^4[/tex]
Adding the like terms in the above expression we get
[tex]=7x^4-20x^2a^2-3a^4[/tex]
Therefore [tex](7x^2+a^2)(x^2-3a^2)=7x^4-20x^2a^2-3a^4[/tex]
Therefore the given multiplied expression is
[tex](7x^2+a^2)(x^2-3a^2)=7x^4-20x^2a^2-3a^4[/tex]
