Question

Find the product. $$(100+27 x)^{2}$$

Short answer

The product of \( (100+27x)^{2} \) is \( 729x^{2} + 5400x + 10000 \).

Step-by-step solution

Apply the binomial square formula

To solve the problem, use the formula for squaring a binomial which is \((a + b)^{2} = a^{2} + 2ab + b^{2}\). In this case, \(a=100\) and \(b=27x\). So apply the formula to get \( (100)^{2} + 2 * 100 * 27x + (27x)^{2} = 10000 + 5400x + 729x^{2} \).

Rearrange the terms

Rearrange the terms from highest power of x to the lowest to get \( 729x^{2} + 5400x + 10000 \). This is the square or product of the given binomial expression \((100+27x)^{2}\).