Question

Subtract the second expression from the first
expression
7y2 - 9x2 + 21xy, 36x2 - 2y2​

Answer 1

Given :-

• 7y² - 9x² + 21xy, 36x² - 2y²

To find :-

• The answer when 36x² - 2y² is subtracted from 7y² - 9x² + 21xy.

Here,

First expression - 7y² - 9x² + 21xy

Second expression - 36x² - 2y²

Equation - 7y² - 9x² + 21xy - 36x² - 2y²

Let's solve your expression step by step:-

$\leadsto$ 32x² - 2y² + -1(7y² + 9x² + 2xy)

$\leadsto$ 32x² - 2y² + -1(7y²) + -1(9x²) + -1(2xy)

$\leadsto$ 32x² - 2y² - 7y² + -1(9x²) + -1(2xy)

$\leadsto$ 32x² - 2y² - 7y² + 9x² + -1(2xy)

$\leadsto$ 36x² + 9x² - 2y² - 7y² - 2xy

$\leadsto$ 45x² - 9y² - 2xy

Therefore, 7y² - 9x² + 21xy - 36x² - 2y² = 45x² - 9y² - 2xy.

Now, Verification :-

We have,

• L.H.S = 36x² - 7y² - 9x² + 21xy
• R.H.S = 45x² - 9y² - 2xy

By evaluating L.H.S :-

$\leadsto$ 32x² - 2y² + -1(7y² + 9x² + 2xy)

$\leadsto$ 32x² - 2y² + -1(7y²) + -1(9x²) + -1(2xy)

$\leadsto$ 32x² - 2y² - 7y² + -1(9x²) + -1(2xy)

$\leadsto$ 32x² - 2y² - 7y² + 9x² + -1(2xy)

$\leadsto$ 36x² + 9x² - 2y² - 7y² - 2xy

$\leadsto$ 45x² - 9y² - 2xy

Now,

L.H.S = 45x² - 9y² - 2xy

R.H.S = 45x² - 9y² - 2xy

Therefore, L.H.S = R.H.S

Hence, Verified!

Answer 2

Step by step explanation:-

$\sf \implies \: 7 {y}^{2} - 9 {x}^{2} + 21xy - 36 {x}^{2} - 2 {y}^{2} \\ \\ \sf \implies \: 7 {y}^{2} + - 9 {x}^{2} + 21xy + - 36 {x}^{2} + - 2 {y}^{2} \\ \\ \sf \implies \: 7 {y}^{2} + - 9 {x}^{2} + 21xy + - 36 {x}^{2} + - 2 {y}^{2} \\ \\ \sf \implies \: ( - 9 {x}^{2} + - 36 {x}^{2} ) + (21xy) + (7 {y}^{2} + - 2 {y}^{2} ) \\ \\ \sf \implies \: - 45 {x}^{2} + 21xy + 5 {y}^{2}$