Question

② $(x + 5)(x - 8)=$
④ $(x + 1)(x - 5)=$
⑥ $(x - 5)(x - 2)=$
⑧ $(y + 3)(y - 3)=$

Explanation:

Step1: Use FOIL method for \((x + 5)(x - 8)\)

\[

$$\begin{align*} &(x+5)(x - 8)\\ =&x\times x+x\times(-8)+5\times x + 5\times(-8)\\ =&x^{2}-8x + 5x-40\\ =&x^{2}-3x - 40 \end{align*}$$

\]

Step2: Use FOIL method for \((x + 1)(x - 5)\)

\[

$$\begin{align*} &(x + 1)(x - 5)\\ =&x\times x+x\times(-5)+1\times x+1\times(-5)\\ =&x^{2}-5x+x - 5\\ =&x^{2}-4x - 5 \end{align*}$$

\]

Step3: Use FOIL method for \((x - 5)(x - 2)\)

\[

$$\begin{align*} &(x - 5)(x - 2)\\ =&x\times x+x\times(-2)+(-5)\times x+(-5)\times(-2)\\ =&x^{2}-2x-5x + 10\\ =&x^{2}-7x + 10 \end{align*}$$

\]

Step4: Use difference - of - squares formula \((a + b)(a - b)=a^{2}-b^{2}\) for \((y + 3)(y - 3)\)

\[

$$\begin{align*} &(y + 3)(y - 3)\\ =&y^{2}-3^{2}\\ =&y^{2}-9 \end{align*}$$

\]

Answer:

For \((x + 5)(x - 8)\): \(x^{2}-3x - 40\)
For \((x + 1)(x - 5)\): \(x^{2}-4x - 5\)
For \((x - 5)(x - 2)\): \(x^{2}-7x + 10\)
For \((y + 3)(y - 3)\): \(y^{2}-9\)