The solution is [tex]49 c^{4}+84 c^{2}+36[/tex]
Explanation:
The expression is [tex]\left(7 c^{2}+6\right)^{2}[/tex]
The square of a binomial is always a trinomial.
To determine the square of a binomial we shall use the formula.
The formula to find the square of a binomial is
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
Let us use this formula to multiply the expression [tex]\left(7 c^{2}+6\right)^{2}[/tex]
Here [tex]a=7c^{2}[/tex] and [tex]b=6[/tex]
Substituting the values in the formula, we get,
[tex]\left(7 c^{2}+6\right)^{2}=\left(7 c^{2}\right)^{2}+2 \cdot 7 c^{2} \cdot 6+6^{2}[/tex]
Squaring each term, we have,
[tex]\left(7 c^{2}+6\right)^{2}=49 c^{4}+2\cdot 7 c^{2} \cdot 6+36[/tex]
Multiplying the product of two terms, we get,
[tex]\left(7 c^{2}+6\right)^{2}=49 c^{4}+84c^{2}+36[/tex]
Thus, the solution is [tex]49 c^{4}+84 c^{2}+36[/tex]
