Question

Tell whether the following statement is true or false . The product of \((a+b)\) and \((a+b)\) is \(a^{2}+b^{2}\) Explain.

Short answer

The statement is false. The correct product of \((a+b)\) and \((a+b)\) is \(a^{2} + 2ab + b^{2}\), not \(a^{2} + b^{2}\)

Step-by-step solution

Identify the Binomials

The binomials in this problem are \((a+b)\) and \((a+b)\). To multiply them, the FOIL method is used. The FOIL method stands for First, Outer, Inner, Last, which is the order in which terms get multiplied when working with binomials.

Apply the FOIL Method

Using the FOIL method, multiply the First terms, then the Outer terms, then the Inner terms, and finally the Last terms. The first terms are 'a' and 'a', the outer terms are 'a' and 'b', the inner terms are 'b' and 'a', and the last terms are 'b' and 'b'. This gives \(a*a + a*b + b*a + b*b\), which simplifies to \(a^{2} + 2ab + b^{2}\).

Conclusion

Comparing this result with the given equation \(a^{2} + b^{2}\), it's clear that they are not the same. Therefore, the original statement that \((a+b) * (a+b) = a^{2} + b^{2}\) is false.