Question

find the value using identities:

(please write the formulas with steps please)

a) (3a+5b)²
b) (2x-y)²
c) (6x+3)(6x+5)
d) (4m-7n)(4m+7n)
e) (3m-7)(3m-4)​

Answer 1

a) ( 3a + 5b ) ²

❥ ( a + b ) ² = a² + 2ab + b²

(3a)² + 2 x 3a x 5b + (5b)²

9a² + 30ab + 25b²

b) ( 2x - y ) ²

❥ ( a - b ) ² = a² - 2ab + b²

(2x)² - 2 x 2x x y + y²

4x² - 4xy + y²

c) ( 6x + 3 ) ( 6x + 5 )

❥ ( x + a ) ( x + b ) = x² + ( a + b ) x + ab

(6x)² + ( 3 + 5 ) 6x + 3 x 5

36x² + 48x + 15

d) ( 4m + 7n ) ( 4m - 7n )

❥ ( a + b ) ( a - b ) = a² - b²

(4m)² - (7n)²

16m² - 49n²

e) ( 3m - 7 ) ( 3m - 4 )

9m² - 12m - 21m + 28

9m² - 33m + 28

Answer 2

a) (3a+5b)²

❥ (a + b)² = a² + 2ab + b²

(3a²) + 2 x 3a x 5b + (5b²)

9a² + 30ab + 25b²

b) (2x-y)²

❥ (a - b)² = a² - 2ab + b²

(2x)² - 2 x 2x x y + y²

4x² - 4xy + y²

c) (6x+3)(6x+5)

❥ (x + a) (x + b) = x² + (a + b) x + ab

(6x)² + (3 + 5) 6x + 3 x 5

36x² + 48x + 15

d) (4m-7n)(4m+7n)

❥ (a + b) (a - b) = a² - b²

(4m)² - (7n)²

16m² - 49n²

e) (3m-7)(3m-4)

9m² - 12m - 21m + 28

9m² - 33m + 28