Tutorial

Topic : Cubic Identities

Expand (x+3)(x+5)(x+2) by using the identity (x+a)(x+b)(x+c)=x³+(a+b+c)x²+(ab+bc+ca)x+abc

Step 1 : (x+3)(x+5)(x+2) (Given Question)

Step 2 : x³+(3+5+2)x²+(3x5+5x2+2x3)x+3x5x2(Compare and Substitute in the place of a,b and c ie., x = x, a = 3, b=5, c=2 )

Step 3 : The first term becomes as it is, because there is no change in the value ie.,x³

Step 4 : The second term becomes a + b + c = 3 + 5 + 2 = 10, then (a +b +c)x²= 10x²

Step 5 : The third term becomes ab + bc + ca = 3 x 5 + 5 x 2 + 2 x 3 = 15 + 10 + 6 = 31, then (ab + bc + ca)x = 31x

Step 6 : The last part of the identity abc or a x b x c = 3 x 5 x 2 = 30

Step 7 : Therefore the answer is x³+10x²+ 31x+30

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