Question

(5X^2 - 2Y^2) X (Y^2+XY^3-8X) MUTIPLY BEST ANSWER WILL BE MARKED BRAINLIEST ^ REPRESENTS POWER PLS PLS

Answer 1

Question:

$\sf (5 {x}^{2} - 2 {y}^{2} )( {y}^{2} + x {y}^{3} - 8x)$

To find:

★ To find the value of the given expression.

Answer:

The value of the given expression $\underline{ \sf 2 {y}^{4} - 5 {x}^{3} {y}^{3} - 5 {x}^{2} {y}^{2} + 2x {y}^{5} - 16x {y}^{2} + 40 {x}^{3} }$

Given:

★ An expression is given.

Step-by-step explanation:

$\sf \bold{(5 {x}^{2} - 2 {y}^{2} )( {y}^{2} + x {y}^{3} - 8x)}$

Now multiplying the polynomials,

$\hookrightarrow \sf (5 {x}^{2} \times {y}^{2} ) + (5 {x}^{2} \times x {y}^{3} ) + (5 {x}^{2} \times - 8x)$

$\hookrightarrow \sf \underline{ 5 {x}^{2} {y}^{2} + 5 {x}^{3} {y}^{3} - 40 {x}^{3} }$

$\hookrightarrow \sf ( - 2 {y}^{2} \times {y}^{2}) + ( - 2 {y}^{2} \times x {y}^{3}) + ( - 2 {y}^{2} \times - 8x)$

$\hookrightarrow \sf \underline{ - 2 {y}^{4} - 2x {y}^{5} + 16x {y}^{2} }$

Now adding the polynomials,

$\implies \sf 5 {x}^{2} {y}^{2} + 5 {x}^{3} {y}^{3} - 40 {x}^{3} - 2 {y}^{4} - 2x {y}^{5} + 16x {y}^{2}$

Now Arranging through powers ,

$\implies \sf - 2 {y}^{4} + 5 {x}^{3} {y}^{3} + 5 {x}^{2} {y}^{2} - 2x {y}^{5} + 16x {y}^{2} - 40 {x}^{3}$

Since first polynomial is in negative now changing to positive .

$\implies \boxed{ \sf 2 {y}^{4} - 5 {x}^{3} {y}^{3} - 5 {x}^{2} {y}^{2} + 2x {y}^{5} - 16x {y}^{2} + 40 {x}^{3} }$

$\therefore$ The value of the given expression is 2y⁴ - 5x³y³ - 5x²y² + 2x$\underline{\bold{{y}^{5}}}$ - 16xy² + 40x³ .