Question

Factorize;Answer the tick one i will mark you as brainlist please quickly step by step explanation also please show it clearly i will mark you as brainlist​

Answer 1

Answer:

use the formula:

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

1) 4a² + 49b²

= 2²a² + 7²b²

= (2a)² + (7b)²

based on the formula above, a = 2a and b = 7b

= ( 2a + 7b )² - 2(2a)(7b)

substitute 2a+7b = 11 into the equation

= 11² - 2( 14ab )

= 121 - 28ab

substitute ab = 2 into the equation

= 121 - 28(2)

= 121 - 56

= 65

2) 4x² + 9y²

= 2²x² + 3²y²

= (2x)² + (3y)²

based on the formula, a = 2x and b = 3y

= ( 2x + 3y )² - 2(2x)(3y)

substitute 2x+3y = 12 into the equation

= 12² - 2(2x)(3y)

= 144 -2(6xy)

= 144 - 12xy

substitute xy = 6 into the equation

= 144 - 12(6)

= 144 - 72

= 72

3) 4x² + 9y²

= 2²x² + 3²y²

= (2x)² + (3y)²

= (2x)² - (-3y)²

based on the formula, a=2x and b=-3y

= ( 2x-3y )²- 2(2x)(-3y)

substitute 2x-3y = 2 into the equation

= (2)² - 2(2x)(-3y)

= 4 - 2( -6xy )

= 4 + 12xy

substitute xy = 8 into the equation

= 4 + 12(8)

= 4 + 96

= 100

4) 16x² + 25y²

= 4²x² + 5²y²

= (4x)² + (5y)²

= (4x)² - (-5y)²

based on the formula, a = 4x and b = -5y

= (4x-5y)² - 2(4x)(-5y)

substitute 4x-5y = 6

= (6)² -2(4x)(-5y)

= 36 -2(-20xy)

= 36 + 40xy

substitute xy = 8 into the equation

= 36 + 40(8)

= 36 + 320

= 356

Answer 2

Answer:

Solved only ticked ones

• 4a² + 49b² = (2a + 7b)² - 28ab = 11² - 28*2 = 65
• 4x² + 9y² = (2x + 3y)² - 12xy = 12² - 12*6 = 72
• 4x² + 9y² = (2x - 3y)² + 12xy = 2² + 12*8 = 100
• 16x² + 25y² = (4x - 5y)² + 40xy = 6² + 40*8 = 356