Question

multiply 7x²y³(2x⁴y⁵+6xy³) with full explanation and steps in English

I want steps what we have to do in 1st step in English then write in maths​

Answer 1

your question:

$\sf2 {x}^{4} {y}^{5} + 6x {y}^{3} \: by \: 7 {x}^{2} {y}^{3}$

To multiply polynomials, multiply each term of the first polynomial by every term of the second polynomial. Then simplify the products and add them. Finally, simplify further if possible.

So, perform the first step:

$\sf( \pink{2 {x}^{4} {y}^{5} } + \red{6x {y}^{3}} ) .( \green{7 {x}^{2} {y}^{3} }) \\ \implies( \sf \pink{2 {x}^{4} {y}^{5} }) \times ( \green{7 {x}^{2} {y}^{3} }) + (\red{6x {y}^{3}} ) \times ( \green{7 {x}^{2} {y}^{3} }) \\ \\ \sf simplify \: products \\ \sf = 14 {x}^{6} {y}^{8} + 42 {x}^{3 } {y}^{6} \\ \\ \mathbb{ANSWER:} \\ \sf(2 {x}^{4} {y}^{5} + 6x {y}^{3} ).( 7 {x}^{2} {y}^{3} ) \\ \sf = \pink 14 \red{x}^{6} \orange{{y}^{8}} + \blue{42 {x}^{3 } {y}}^ \green{6}$

Answer 2

your question:

$\huge{\sf{(2x⁴y⁵+6xy³)by 7x²y³}}$

To multiply polynomials, multiply each term of the first polynomial by every term of the second polynomial. Then simplify the products and add them. Finally, simplify further if possible.

So, perform the first step:

$\huge{\sf{(2x⁴y⁵+6xy³).( 7x²y³)}}$

$\huge{\sf{\rightarrow{(2x⁴y⁵)×( 7x²y³)+(6xy³)×(7x²y³)}}}$

$\huge{\sf{simplify products}}$

$\huge{\sf{=14x^6y^8+42x³y^6}}$

$\huge{\underline{\boxed{\tt{answer!}}}}$

$\huge{\sf{(2x⁴y⁵+6xy³).( 7x²y³)}}$

$\huge{\sf{=14x^6y^8+42x³y^6}}$