Question

8 which of the following expressions would have a product of $p^{2}-2pq + q^{2}$?
g. $(p - q)^{2}$
h. $(p + q)^{2}$
i. $(p + q)(p - q)$
j. $(p + q)(2p - q)$

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\), and for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Also, the formula for \((a + b)(a - b)\) is \(a^2 - b^2\).

Step2: Expand each option

• For option G: \((p - q)^2\), using the formula \((a - b)^2=a^2 - 2ab + b^2\) with \(a = p\) and \(b=q\), we get \(p^2-2pq + q^2\).
• For option H: \((p + q)^2=p^2 + 2pq+q^2\) (using \((a + b)^2=a^2 + 2ab + b^2\) with \(a = p\) and \(b = q\)).
• For option I: \((p + q)(p - q)=p^2 - q^2\) (using the difference of squares formula).
• For option J: \((p + q)(2p - q)=2p^2 - pq+2pq - q^2=2p^2+pq - q^2\) (by multiplying each term in the first binomial with each term in the second binomial).

Answer:

G. \((p - q)^2\)