Question

Q.12 Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products.

(i) (4x + 9) (4x + 12)

(ii) (x - 5) (x - 1)​

Answer 1

$\sf \bold{→(4x+9)(4x+12)}$

Here,

• x = 4x
• a = 9
• b = 12

So,

$\begin{gathered} \rightarrow \sf \: {(4x)}^{2} + (9 + 12)(4x) + 9 \times 12 \\ \\ \rightarrow \sf \: 16 {x}^{2} + 21(4x) + 108 \\ \\ \rightarrow \boxed{ \tt{ \green{16 {x}^{2} + 84x + 108 }}}\end{gathered}$

Question 2

$\rightarrow \sf \: \red{ (x - 5)(x - 1)}$

Here,

• x = x
• a = -5
• b = -1

so,

$\begin{gathered} \rightarrow \sf \: {x}^{2} + \{( - 5) + ( - 1) \} + \{ ( - 5)( - 1) \}x \\ \\ \rightarrow \sf \: {x}^{2} + ( - 5 - 1)x + (5) \\ \\ \rightarrow \sf \: {x}^{2} + ( - 6)x + 5 \\ \\ \rightarrow \boxed{ \tt{ \purple{ {x}^{2} - 6x + 5}}}\end{gathered}$

Hence, This is Answer.