Question

solve using identities

Answer 1

Hi here is your answer.

Answer 2

Given

$1.(x + 4)(x + 10) \\ \\ 2.(x + 8)(x - 10) \\ \\ 3.(3x + 4)(3x - 5) \\ \\ 4. \bigg({y}^{2} + \frac{3}{2} \bigg) \bigg({y}^{2} - \frac{3}{2} \bigg) \\ \\ 5.(3 - 2x)(3 + 2x)$

To find

• the following products.

Using

• suitable identities.

Solution

No.1

$\large \rm{ \green{1.(x + 4)(x + 10)}} \\ \\ \bigg[ \small{ \frac{ \bf{using \: formula \: :}}{ \rm(x + a)(x + b) = {x}^{2} + (a + b)x + ab} } \bigg] \\ \\ = x(x + 10) + 4(x + 10) \\ = {x}^{2} +10x + 4x + (10 \times 4) \\ = {x}^{2} + 14x + 40 \\ \\ \large \rm \red{= {x}^{2} + 14x + 40}$

No.2

$\large \rm{ \green{1.(x + 8)(x - 10)}} \\ \\ \bigg[ \small{ \frac{ \bf{using \: formula \: :}}{ \rm(x + a)(x + b) = {x}^{2} + (a + b)x + ab} } \bigg] \\ \\ = (x + 8)[ {x + ( - 10)]} \\ = {x}^{2} + \: [ {8 + ( - 10)]}x + 8 \times ( - 10) \\ = {x}^{2} + (8 - 10)x - 80 \\ = {x}^{2} - 2x - 80 \\ \\ \large \rm \red{= {x}^{2} - 2x - 80}$

No.3

$\large \rm{ \green{3.(3x + 4)(3x - 5)}} \\ \\ \bigg[ \small{ \frac{ \bf{using \: formula \: :}}{ \rm(x + a)(x + b) = {x}^{2} + (a + b)x + ab} } \bigg] \\ \\ = (3x + 4)[ {3x + ( - 5)]} \\ = {9x}^{2} + \: [ {4 + ( - 5)]}3x + 4 \times ( - 5) \\ = {9x}^{2} + ( - 3x) - 20 \\ = {9x}^{2} - 3x - 20 \\ \\ \large \rm \red{= {9x}^{2} - 3x - 20}$

No.4

$\large \rm{ \green{4. \bigg({y}^{2} + \frac{3}{2} \bigg) \bigg({y}^{2} - \frac{3}{2} \bigg)}} \\ \\ \bigg[ \small{ \frac{ \bf{using \: formula \: :}}{ \rm(a + b)(a - b) = {a}^{2} - {b}^{2} } } \bigg] \\ \\ = {y}^{2} \bigg( {y}^{2} - \frac{3}{2} \bigg) + \frac{3}{2} \bigg( {y}^{2} - \frac{3}{2} \bigg) \\ = { \bigg( {y}^{2} \bigg)}^{2} - \frac{3 {y}^{2} }{2} + \frac{ {3y}^{2} }{2} - \bigg( \frac{3}{2} \bigg) \\ = { \bigg( {y}^{2} \bigg)}^{2} - \cancel \frac{3 {y}^{2} }{2} + \cancel \frac{ {3y}^{2} }{2} - \bigg( \frac{3}{2} \bigg) \\ = {y}^{4} - \frac{9}{4} \\ \\ \large \rm \red{= {y}^{4} - \frac{9}{4} }$

No.5

$\large \rm{ \green{5. (3-2x)(3+2x)}} \\ \\ \bigg[ \small{ \frac{ \bf{using \: formula \: :}}{ \rm(a + b)(a - b) = {a}^{2} - {b}^{2} } } \bigg] \\ \\ = 3(3 - 2x) + 2x(3 - 2x) \\ = 9 - x + x - {4x}^{2} \\ = 9 - \cancel x + \cancel x - {4x}^{2} \\ = 9 - {4x}^{2} \\ \\ \large \rm \red{ \: = 9 - {4x}^{2} }$