Free Printable Binomial Expansions

1.

Expand $\left(x+y^3\right)^4$

a)

$x^4+4x^3y^3+6x^2y^6+4xy^9+y^{12}$

b)

$x^4+x^3y^3+x^2y^6+xy^9+y^{12}$

c)

$6x^4+15x^3y^3+20x^2y^6+15xy^9+6y^{12}$

d)

$x^4+4x^3y^3+4x^2y^6+4xy^9+y^{12}$

2.

Expand $\left(u^2-2\right)^3$

a)

$u^6-6u^4+12u^2-8$

b)

$u^6-16u^4+12u^2-8$

c)

$5u^6-20u^4+40u^2-40$

d)

$u^6-24u^4+12u^2-8$

3.

Expand $\left(4x-y\right)^3$

a)

$64x^3-48x^2y+12xy^2-y^3$

b)

$64x^3-16x^2y+4xy^2-y^3$

c)

$256x^3-96x^2y+16xy^2-y^3$

d)

$320x^3-160x^2y+40xy^2-5y^3$

4.

Expand $\left(4n-1\right)^4$

a)

$256n^4-256n^3+96n^2-16n+1$

b)

$1280n^4-640n^3+160n^2-20n+1$

c)

$1536n^4-960n^3+320n^2-60n+6$

d)

$256n^4-64n^3+16n^2-4n+1$

5.

Expand $\left(2y+x\right)^5$

a)

$32y^5+80y^4x+80y^3x^2+40y^2x^3+10yx^4+x^5$

b)

$192y^5+240y^4x+160y^3x^2+60y^2x^3+12yx^4+x^5$

c)

$32y^5+16y^4x+8y^3x^2+4y^2x^3+2yx^4+x^5$

d)

$2224y^5+336y^4x+280y^3x^2+140y^2x^3+42yx^4+7x^5$

6.

Find the term containing $u^2$ in the expansion of $\left(u-3\right)^5$

a)

$-270u^2$

b)

$90u^2$

c)

$-27u^2$

d)

$405u^2$

7.

Find the term containing $x^5$ in the expansion of $\left(2y+x\right)^7$

a)

$84y^2x^5$

b)

$280y^3x^5$

c)

$672y^2x^5$

d)

$14y^3x^5$

8.

Find the term containing $m^5$ in the expansion of $\left(2m+3\right)^7$

a)

$6048m^5$

b)

$288m^5$

c)

$2016m^5$

d)

$20412m^5$

9.

Find the term containing $y^3$ in the expansion of $\left(y+2\right)^6$

a)

$160y^3$

b)

$8y^3$

c)

$120y^3$

d)

$56y^3$

10.

Find the term containing $b^3$ in the expansion of $\left(b-2\right)^6$

a)

$-160b^3$

b)

$-80b^3$

c)

$-20b^3$

d)

$4b^3$

Binomial Expansions

Total questions: 10

Worksheet time: 30mins

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