Phân tích đa thức thành nhân tử
a) $-x^{2}$ + 10x – 25
b) $-16a^{4}$$b^{6}$ – $24a^{5}$$b^{5}$ – $9a^{6}$$b^{4}$
c) $25x^{2}$ – 20xy + $4y^{2}$
d) $25x^{4}$ – 10$x^{2}$y + $y^{2}$
Phân tích đa thức thành nhân tử a) $-x^{2}$ + 10x – 25 b) $-16a^{4}$$b^{6}$ – $24a^{5}$$b^{5}$ – $9a^{6}$$b^{4}$ c) $25x^{2}$ – 20xy + $4y^{2}$
By Aaliyah
Đáp án:
a, – x² + 10x – 25
= – ( x² – 10x + 25)
= – (x² – 2.5x + 5² )
= – (x – 5)²
b, $-16a^{4}$ $b^{6}$ – $24a^{5}$ $b^{5}$ – $9a^{6}$ $b^{4}$
= – $a^{4}$ $b^{4}$.($16b^{2}$ + $24ab$ + $9a^{2}$)
= – $a^{4}$ $b^{4}$.(4b +3a)²
c, 25x² – 20xy + 4y²
= (5x)² – 2.5.2xy + (2y)²
= (5x – 2y)²
d, $25x^{4}$ – $10x^{2}y$ + $y^{2}$
= (5x²)² – 2.5x²y + y²
= (5x² – y)²
Đáp án:
a, `-x^2 + 10x – 25`
` = -(x^2 – 10x + 25)`
` = -(x – 5)^2`
b, `-16a^4b^6 – 24a^5b^5 – 9a^6b^4`
` = a^4b^4(-16b^2 – 24ab – 9a^2)`
` = a^4b^4. -(16b^2 + 24ab + 9a^2)`
` = -a^4b^4.[(4b)^2 + 2.4b.3a + (3a)^2]`
` = -a^4b^4(4b + 3a)^2`
c, `25x^2 – 20xy + 4y^2`
` = (5x)^2 – 2.5x.2y + (2y)^2`
` = (5x – 2y)^2`
d, `25x^4 – 10x^2y + y^2`
` = (5x^2)^2 – 2.5x^2.y + y^2`
` = (5x^2 – y)^2`
Giải thích các bước giải: