Question

Mulitply 5p²+25pq+4q² by 2p²-2pq+3q²​

Answer 1

$( {5p}^{2} + 25pq + {4q}^{2} )( {2p}^{2} - 2pq + {3q}^{2} )$

$= {5p}^{2} ( {2p}^{2} - 2pq - {3q}^{2} ) + 25pq( {2p}^{2} - 2pq - {3q}^{2} ) {4q}^{2} ( {2p}^{2} - 2pq - {3q}^{2} )$

$= {10p}^{4} - 10 {p}^{3} q - 15 {p}^{2} {q}^{2} + 50 {p}^{3} q - 50 { {p}^{2} } {q}^{2} + 75p {q}^{3} + 8 {p ^{2} } {q}^{2} - 8p {q}^{3} + 12 {q}^{4}$

$= {10p}^{4} - 10 {p}^{3} + 50 {p}^{3} q - 15 {p {}^{2} } {q}^{2} - 50 {p}^{2} {q}^{2} + 8 {p}^{2} {q}^{2} + 75p {q}^{3} - 8p {q}^{3} + 12 {q}^{4}$

$= {10p}^{4} + 40 {p}^{3} q - 57 { {p}^{2} } {q}^{2} + 67p {q}^{3} + 12 {q}^{4}$

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