Question

The square of 4x-5y is​

Answer 1

Step-by-step explanation:

16x2−40xy+25y2

We have, (4x−5y)2=(4x)2−2(4x)(5y)+(5y)2

=16x2−40xy+25y2

Answer 2

Answer:

4x² + 5y² - 40xy

Step-by-step explanation:

$(4x - 5y) {}^{2} \\ \\ { \tt {Derivations}} \begin{cases} { \rm\red{(a - b) {}^{2} }}\\ { \rm \red{(a + b) {}^{2} }} \end{cases} \\ \\ \: {\tt \green{(a - b) {}^{2} }} \: \: \: \: \tt \blue { \implies} \: a {}^{2} + b {}^{2} - 2ab \\ \: {\tt \green{(a + b) {}^{2} }} \: \: \: \: \tt \blue { \implies} \: a {}^{2} + b {}^{2} + 2ab \\ \\ \\ \rm \: (4x - 5y) {}^{2} \\ \\ \implies4x {}^{2} + 5y {}^{2} - 2(4x \times 5y) \\ \\ \implies4x {}^{2} + 5y {}^{2} - 2 \times 20xy \\ \\ \implies4x {}^{2} + 5y {}^{2} - 40xy$

So the answer of your question is 4x² + 5y² - 40xy.

Other examples:-

• (2x + 3y) ²

$(2x + 3y) {}^{2} \\ \\ { \tt {Derivations}} \begin{cases} { \rm\red{(a - b) {}^{2} }}\\ { \rm \red{(a + b) {}^{2} }} \end{cases} \\ \\ \: {\tt \green{(a - b) {}^{2} }} \: \: \: \: \tt \blue { \implies} \: a {}^{2} + b {}^{2} - 2ab \\ \: {\tt \green{(a + b) {}^{2} }} \: \: \: \: \tt \blue { \implies} \: a {}^{2} + b {}^{2} + 2ab \\ \\ \\ \rm \: (2x + 3y) {}^{2} \\ \\ \implies2x {}^{2} + 3y {}^{2} + 2(2x \times 3y) \\ \\ \implies2x {}^{2} + 3y {}^{2} + 2 \times 6xy \\ \\ \implies2x {}^{2} + 3y {}^{2} - 12xy$

Thanks