Square

Algebra Level 1

Expand ( 2 x − 3 y ) 2 . \large (2x-3y)^2 .

4 x 2 + 12 x y − 9 y 2 4x^2+12xy-9y^2 4 x 2 − 12 x y + 9 y 2 4x^2-12xy+9y^2 0 4 x 2 + 12 x y + 9 y 2 4x^2+12xy+9y^2

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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4 solutions

Md Zuhair
Mar 23, 2017

The Answer will follow, ( a − b ) 2 = a 2 − 2 a b + b 2 (a-b)^2=a^2-2ab+b^2 formula

( 2 x − 3 y ) 2 (2x-3y)^2

= ( 2 x ) 2 − 2.2 x . 3 y + ( 3 y ) 2 (2x)^2-2.2x.3y+(3y)^2

= 4 x 2 − 12 x y + 9 y 2 4x^2-12xy+9y^2

4 x 2 − 12 x y + 9 y 2 \boxed{4x^2-12xy+9y^2}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Munem Shahriar
Mar 23, 2017

This question will follow, ( a − b ) 2 = a 2 − 2 a b + b 2 (a - b)^2 = a^2 - 2ab + b^2 formula

( 2 x − 3 y ) 2 (2x - 3y)^2

= ( 2 x ) 2 − 2 ⋅ 2 x ⋅ 3 y + ( 3 y ) 2 = (2x)^2 - 2 \cdot 2x \cdot 3y + (3y)^2

= 4 x 2 − 12 x y + 9 y 2 =4x^2 - 12xy + 9y^2

Answer: 4 x 2 − 12 x y + 9 y 2 4x^2 - 12xy + 9y^2

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Jul 18, 2017

( 2 x − 4 y ) 2 {(2x -4y)} ^{2} = ( 2 x ) 2 {(2x)}^{2} - 2 × 2 x × 3 y 2 \times 2x \times 3y + ( 3 y ) 2 {(3y)}^{2} = 4 x 2 4x^2 - 12 x y 12xy + 9 y 2 9y^2

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Fahim Saikat
Aug 19, 2017

( 2 x − 3 y ) 2 = ( 2 x − 3 y ) × ( 2 x − 3 y ) = ( 2 x ) × ( 2 x ) + ( 2 x ) × ( − 3 x ) + ( 2 x ) × ( − 3 x ) + ( − 3 x ) × ( − 3 x ) = 4 x 2 − 12 x y + 9 y 2 \begin{aligned}(2x-3y)^2&=(2x-3y)\times(2x-3y)\\&=(2x)\times(2x)+(2x)\times(-3x)+(2x)\times(-3x)+(-3x)\times(-3x)\\&=\boxed{4x^2-12xy+9y^2}\end{aligned}

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