Question

Use the binomial squares pattern to multiply (7c²+6)²

Answer 1

The solution is $49 c^{4}+84 c^{2}+36$

Explanation:

The expression is $\left(7 c^{2}+6\right)^{2}$

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

$(a+b)^{2}=a^{2}+2 a b+b^{2}$

Let us use this formula to multiply the expression $\left(7 c^{2}+6\right)^{2}$

Here $a=7c^{2}$ and $b=6$

Substituting the values in the formula, we get,

$\left(7 c^{2}+6\right)^{2}=\left(7 c^{2}\right)^{2}+2 \cdot 7 c^{2} \cdot 6+6^{2}$

Squaring each term, we have,

$\left(7 c^{2}+6\right)^{2}=49 c^{4}+2\cdot 7 c^{2} \cdot 6+36$

Multiplying the product of two terms, we get,

$\left(7 c^{2}+6\right)^{2}=49 c^{4}+84c^{2}+36$

Thus, the solution is $49 c^{4}+84 c^{2}+36$