Question

В)(y^2-3y-2)(y^2+3y-2) г)(a+2b+3c)(2a-b+2c)

Answer 1

=у∧4+3у∧3-2у∧2-3у∧3-9у∧2+6у-2у∧2-6у+4=у∧4-13у∧2+4
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=2а∧2-аб+2ас+4аб-2б∧2+4бс+6ас-3бс+6с∧2=2а∧2+3аб+8ас-2б∧2+бс+6с∧2

Answer 2

To multiply the given expressions, we'll use the distributive property and combine like terms:

a) Multiply (y^2 - 3y - 2) by (y^2 + 3y - 2):

(y^2 - 3y - 2)(y^2 + 3y - 2) = y^2(y^2 + 3y - 2) - 3y(y^2 + 3y - 2) - 2(y^2 + 3y - 2)

Expanding each term:

= (y^4 + 3y^3 - 2y^2) - (3y^3 + 9y^2 - 6y) - (2y^2 + 6y - 4)

Now, combine like terms:

= y^4 + 3y^3 - 2y^2 - 3y^3 - 9y^2 + 6y - 2y^2 - 6y + 4

= y^4 - 9y^2 - 2y^2 + 3y^3 - 3y^3 + 6y - 6y + 4

Simplifying:

= y^4 - 11y^2 + 4

Therefore, the result of (y^2 - 3y - 2)(y^2 + 3y - 2) is y^4 - 11y^2 + 4.

b) Multiply (a + 2b + 3c) by (2a - b + 2c):

(a + 2b + 3c)(2a - b + 2c) = a(2a - b + 2c) + 2b(2a - b + 2c) + 3c(2a - b + 2c)

Expanding each term:

= 2a^2 - ab + 2ac + 4ab - b^2 + 4bc + 6ac - 3bc + 6c^2

Now, combine like terms:

= 2a^2 + 4ab - ab - b^2 + 2ac + 6ac + 4bc - 3bc + 6c^2

= 2a^2 + 3ab - b^2 + 8ac + bc + 6c^2

Therefore, the result of (a + 2b + 3c)(2a - b + 2c) is 2a^2 + 3ab - b^2 + 8ac + bc + 6c^2.