An algebra problem by Andriane Casuga

Algebra Level 1

What is (2+y)³ written out?

6 + 8y + 4y² + y³ 8 + 12y + 6y² + y³

Andriane Casuga by Andriane Casuga , 30, United Arab Em…

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3 solutions

( 2 + y ) 3 = 2 3 + 3 × 2 2 y + 3 × 2 y 2 + y 3 = 8 + 12 y + 6 y 2 + y 3 (2+y)^3 = 2^3+3\times 2^2 y+3 \times 2y^2+y^3=\boxed{8+12y+6y^2+y^3}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

We can use the identity: ( x + y ) 3 = x 3 + 3 x 2 y + 3 x y 2 + y 3 (x+y)^3=x^3+3x^2y+3xy^2+y^3

S0,

( 2 + y ) 3 = 2 3 + 3 ( 2 2 ) ( y ) + 3 ( 2 ) ( y 2 ) + y 3 = 8 + 12 y + 6 y 2 + y 3 (2+y)^3=2^3+3(2^2)(y)+3(2)(y^2)+y^3=\boxed{8+12y+6y^2+y^3}

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Andriane Casuga
Aug 23, 2015

The trick to this one is spotting that 2³=8, though that’s not as fun as multiplying the whole thing out of course.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You don't actually have to multiply out the whole thing.You can just use , ( a + b ) 3 = a 3 + 3 a b ( a + b ) + b 3 (a+b)^{3} = a^3 + 3ab(a+b) +b^3

Athiyaman Nallathambi - 5 years, 9 months ago

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