Question

Use suitable identity to find each of rhe following product: 1= (3x-7)(3x-7). 2= (2/3m + 3/2n)(2/3m -3/2n)​

Answer 1

Answer:

1.  $9x^{2} -42x+49$

2. $4m-9n$

Step-by-step explanation:

1

$=(3x-7)(3x-7)\\=(3x-7)^{2}\\=(3x)^{2} -2*3x*-7+(7)^{2}\\=9x^{2} -42x+49$

2

$=(\frac{2}{3} m+\frac{3}{2} n)(\frac{2}{3} m-\frac{3}{2} n)\\\\=(\frac{2}{3}m - \frac{3}{2}n )\\\\=(\frac{2}{3} m*\frac{2}{2} -\frac{3}{2} *\frac{3}{3} )\\\\=(\frac{4}{6} m -\frac{9}{6} n)\\\\=(4m-9n)\\\\=4m-9n$

Answer 2

Step-by-step explanation:

1. The identity

$(a - b)(a - b) = {a}^{2} - 2ab + {b}^{2}$

can be used

Here a = 3x

b = 7

${(3x)}^{2} - 2(3x)(7) + {7}^{2}$

$9 {x}^{2} - 42x + 49$

2. The identity

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

can be used

Here

$a = \frac{2m}{3} \: \: b = \frac{3n}{2}$

${( \frac{2m}{3} )}^{2} - { (\frac{3n}{2}) }^{2}$

$= \frac{4 {m}^{2} }{9} - \frac{ 9{n}^{2} }{4}$