Factor the expression given below. Write each factor as a polynomial in descending order. Enter exponents using the caret ( ^ ). For example, you would enter x2 as x^2.
27x3 + 343y3
factor this expression in mathematics?
2009-02-18 3:31 pm
回答 (5)
2009-02-18 3:48 pm
✔ 最佳答案
27x^3 + 343y^3=(3x+7y)(9x^2-21xy+49y^2) answer//
2009-02-18 4:05 pm
We know that,
a^3+b^3 = (a+b)(a^2-ab+b^2)
Given that,
27x^3+343y^3
= (3x)^3 + (7y)^3
=(3x+7y){(3x)^2-(3x)(7y)+(7y)^2}
= (3x+7y)(9x^2-21xy+49y^2)
So the factors of the problem are (3x+7y) and (9x^2-21xy+49y^2).
a^3+b^3 = (a+b)(a^2-ab+b^2)
Given that,
27x^3+343y^3
= (3x)^3 + (7y)^3
=(3x+7y){(3x)^2-(3x)(7y)+(7y)^2}
= (3x+7y)(9x^2-21xy+49y^2)
So the factors of the problem are (3x+7y) and (9x^2-21xy+49y^2).
2009-02-18 3:41 pm
27x^3 + 343y^3
= (3x)^3 + (7y)^3
Notice that this is a sum of two cubes.
a^3 + b^3 = (a + b) (a^2 - ab + b^2)
So, (3x)^3 + (7y)^3 = ((3x) + (7y)) ((3x)^2 - (3x)(7y) + (7y)^2)
= (3x + 7y) (9x^2 - 21xy + 49y^2).
^_^
= (3x)^3 + (7y)^3
Notice that this is a sum of two cubes.
a^3 + b^3 = (a + b) (a^2 - ab + b^2)
So, (3x)^3 + (7y)^3 = ((3x) + (7y)) ((3x)^2 - (3x)(7y) + (7y)^2)
= (3x + 7y) (9x^2 - 21xy + 49y^2).
^_^
2009-02-18 3:38 pm
27x^3+343y^3=
(3x)^3+(7y)^3=
(3x+7y)(9x^2-21xy+49y^2)
(3x)^3+(7y)^3=
(3x+7y)(9x^2-21xy+49y^2)
2009-02-18 3:35 pm
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
27x^3 + 343y^3
= (3x)^3 + (7y)^3
= [3x + 7y][(3x)^2 - (3x)(7y) + (7y)^2]
= [3x + 7y][9x^2 - 21xy + 49y^2]
27x^3 + 343y^3
= (3x)^3 + (7y)^3
= [3x + 7y][(3x)^2 - (3x)(7y) + (7y)^2]
= [3x + 7y][9x^2 - 21xy + 49y^2]
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