a) (x+3) (x^2+3x-5) b) (x^3-2x^2+x-1) (5-x) c) (x+2) (4^2-2x^3-8x+16) d) (x^2-4x+6) ( 2x^2-3x-4) 28/11/2021 Bởi Raelynn a) (x+3) (x^2+3x-5) b) (x^3-2x^2+x-1) (5-x) c) (x+2) (4^2-2x^3-8x+16) d) (x^2-4x+6) ( 2x^2-3x-4)
Đáp án: a) \({x^3} + 6{x^2} + 4x – 15\) Giải thích các bước giải: \(\begin{array}{l}a)(x + 3)({x^2} + 3x – 5)\\ = {x^3} + 3{x^2} – 5x + 3{x^2} + 9x – 15\\ = {x^3} + 6{x^2} + 4x – 15\\b)({x^3} – 2{x^2} + x – 1)(5 – x)\\ = 5{x^3} – 10{x^2} + 5x – 5 – {x^4} + 2{x^3} – {x^2} + x\\ = – {x^4} + 7{x^3} – 11{x^2} + 6x – 5\\c)(x + 2)({4^2} – 2{x^3} – 8x + 16)\\ = (x + 2)(16 – 2{x^3} – 8x + 16)\\ = \left( {x + 2} \right)\left( { – 2{x^3} – 8x + 32} \right)\\ = – 2{x^4} – 4{x^3} – 8{x^2} – 16x + 32x + 64\\ = – 2{x^4} – 4{x^3} – 8{x^2} + 16x + 64\\d)({x^2} – 4x + 6)(2{x^2} – 3x – 4)\\ = 2{x^4} – 3{x^3} – 4{x^2} – 8{x^3} + 12{x^2} + 16x + 12{x^2} – 18x – 24\\ = 2{x^4} – 11{x^3} + 20{x^2} – 2x – 24\end{array}\) Bình luận
Đáp án:
a) \({x^3} + 6{x^2} + 4x – 15\)
Giải thích các bước giải:
\(\begin{array}{l}
a)(x + 3)({x^2} + 3x – 5)\\
= {x^3} + 3{x^2} – 5x + 3{x^2} + 9x – 15\\
= {x^3} + 6{x^2} + 4x – 15\\
b)({x^3} – 2{x^2} + x – 1)(5 – x)\\
= 5{x^3} – 10{x^2} + 5x – 5 – {x^4} + 2{x^3} – {x^2} + x\\
= – {x^4} + 7{x^3} – 11{x^2} + 6x – 5\\
c)(x + 2)({4^2} – 2{x^3} – 8x + 16)\\
= (x + 2)(16 – 2{x^3} – 8x + 16)\\
= \left( {x + 2} \right)\left( { – 2{x^3} – 8x + 32} \right)\\
= – 2{x^4} – 4{x^3} – 8{x^2} – 16x + 32x + 64\\
= – 2{x^4} – 4{x^3} – 8{x^2} + 16x + 64\\
d)({x^2} – 4x + 6)(2{x^2} – 3x – 4)\\
= 2{x^4} – 3{x^3} – 4{x^2} – 8{x^3} + 12{x^2} + 16x + 12{x^2} – 18x – 24\\
= 2{x^4} – 11{x^3} + 20{x^2} – 2x – 24
\end{array}\)