Question

Add the given polynomials:
$7 {x}^{4} - 2 {x}^{3} + x + 10: 3 {x}^{4} + 15 {x}^{3} + 9 {x}^{2} - 8x + 2 \\ \\ \\ 3 {p}^{3}q + 2 {p}^{2} q + 7 : 2 {p}^{2} q + 4pq - 2 {p}^{3} q$

Answer 1

ANSWER:

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Answer 1.


$(7 {x}^{4} - 2{x}^{3} + x + 10) ( 3 {x}^{4} + 15 {x}^{3} + 9 {x}^{2} - 8x + 2) \\ \\ = 7x^{4} - 2x {}^{3} + x + 10 + 3 {x}^{4} + 15 {x}^{3} + 9 {x}^{2} - 8x + 2.........(removing \: the \: brackets) \\ \\ = 7 {x}^{4} + 3 {x}^{4} - 2 {x}^{3} + 15 {x}^{3} + 9 {x}^{2} + x - 8x + 10 + 2........(bringing \: the \: like \: terms \: together) \\ \\ =10 {x}^{4} + 13 {x}^{3} + 9 {x}^{2} - 7x + 12. \\ \\ answer:10x {}^{4} + 13 {x}^{3} + 9 {x}^{2} - 7x + 12$
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Answer 2.


$(3p {}^{3}q + 2p {}^{2} q + 7)(2p {}^{2} q + 4pq - 2p {}^{3} q) \\ \\ = 3p {}^{3}q + 2p {}^{2}q + 7 + 2p {}^{2}q + 4pq - 2 {p}^{3} q \\ \\ = 3p {}^{3}q - 2p {}^{3}q + 2p {}^{2}q + 2p {}^{2} q + 4pq + 7 .....(bringng \: the \: like \: terms \: together)\\ \\ = p {}^{3} q + 4p {}^{2} q + 4pq + 7 \\ \\ answer: p {}^{3}q + 4p {}^{2} q + 4pq + 7$