Expand the following with step by step ans

1. (4 + x)^3
2. (6 + x)^3
3. (x + 2)^4
4. (x2 + 3)^3
5. (x2 + 3)^4
6. ( 3m2 + 1)^3
7. ( 2x3 – 3)^4
8. ( 2x3 – 3)^5
9. (x - 2)^5
10 . ( 3m2 - n)^5


thanks in advance

(a + b)^3 = a^3 + b^3 + 3ab^2 + 3a^2b

So. 1) 4^3 + x^3 + 12x^2 + 48x
= 64 + x^3 + 12x^2 + 48x

2) 216 + x^3 + 18x^2 + 108x
3) (x + 2)^2 (x + 2)^2
= (x^2 + 4 + 4x) (x^2 + 4 + 4x)
= x^4 + 4x^2 + 4x^3 + 4x^2 + 16 + 16x + 4x^3 + 16x + 16x^2
= x^4 + 24x^2 + 8x^3 + 32x + 16

4) Use same method as in 1) & 2)
5) Use same method as in 3)
6) Use same method as in 1) & 2)
7) Use the identity (a-b)^2 = a^2 + b^2 - 2ab twice and the multiply the terms obtained and then add the like terms
8) Multiply ( 2x3 – 3), 5 times by using identity (a-b)^2 = a^2 + b^2 - 2ab and then multiply the two terms and then add the like terms. Again multiply the obtained polynomial by ( 2x3 – 3) because the term obtained is after multiplying it 4 times.
9) Same method as in 8)
10) Same method as in 8)



Hope it helps

HAVE A NICE DAY :)

you can write direct answer by using Pascal triangle
. (4 + x)^3 use (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
= (4)^3 + 3(4)^2(x) + 3(4)(x^2) + (x)^3
= 64 + 48x + 12x^2 + x^3

(a + b)^4 = there are 5 terms
coefficients are of 5 terms 1 4 6 4 1
1a^4 + 4a^3b + 6a^2b^2 + 4aB^4 1b^4
(x + 2)^4
= (x)^4 + 4(x^3)(2) + 6(x^2)(2^2) + 4x(2)^3 + (2)^4
= (x^4 + 8(x^3 + 24x^2) + 32x + 16

(a – b)^5 there are 6 terms
coefficients of 6 terms 1 5 10 10 5 1
= (a)^5 – 5(a^4)(b) + 10(a^3)(b^2) – 10(a^2)(b^3) + 5(a)(b^4) – b^5
( 2x^3 – 3)^5
= (2x^3)^5 – 5(2x^3)^4)(3) + 10(2x^3)^3)(3^2) – 10(2x^3)^2)(3^3) + 5(2x^3)(3^4) – 3^5
= (32x^15 – 240x^12 + 180(2x^9 – 1080x^6 + 810x^3 – 81
similarly try others
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See

http://www.mathsisfun.com/pascals-triang…

1. For power 3 expressions, coefficients are 1 3 3 1

(4 + x)^3 = 4^3 + 3*4^2 * x + 3*4^1 *x^2 + x^3

= 64 + 48x + 12x^2 + x^3

It looks complex, but if you learn your PASCAL TRIANGLE, you'd be laughing!

(x+a)^n=(nc0)x^n+(nc1)x^(n-1) a+(nc2)x^(n-2)a^2+---+(ncn)a^n apply this formula