Multiplication of Any Polynomial

Q.

Find the product using a suitable identity: $\left(x+3\right)\left(x-3\right)$

Q.

What is the expanded form of ${\left(x-y\right)}^3$?

Q. Find the square root of 12321.

1. 131
2. 111
3. 121
4. 21

Q.

Maximum value of ${\left(\frac{1}{x}\right)}^x$ is

1. ${\left(e\right)}^e$

2. ${\left(e\right)}^{\frac{1}{e}}$

3. ${\left(e\right)}^{-e}$

4. ${\left(\frac{1}{e}\right)}^e$

Q.

If ${\left(10\right)}^9+2{\left(11\right)}^1{\left(10\right)}^8+3{\left(11\right)}^2{\left(10\right)}^7+.........+10{\left(11\right)}^9=k{\left(10\right)}^9,$ then $k$ is equal to

1. $100$

2. $110$

3. $\frac{121}{100}$

4. $\frac{441}{100}$

Q.

If $y=a{x}^{n+1}+b{x}^{-n}$, then $x^2\frac{d^{2}y}{d{x}^2}=$

1. $n\left(n-1\right)y$

2. $n\left(n+1\right)y$

3. $ny$

4. $n^{2}y$

Q.

Question 3(iv)
Simplify:
(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)

Q.

Question 3(i)
Simplify:
$(x^2-5)(x+5)+25$

Q.

On dividing${\text{x}}^3-3{\text{x}}^2\text{+x+2}$ by a polynomial$\text{g}\left(x\right)$, the quotient and remainder were respectively$\text{x-2 and -2x+4}$respectively. Find$\text{g}\left(x\right)$.

Q.

Write the coefficients of $x^2$ in: $2-x^2+x^3$

Q.

Multiply:

$(5x+3)by(7x+2)$

Q.

Add: $2x(z-x-y)and2y(z-y-x)$

Q.

Multiply :

$\left(i\right)8a{b}^{2}by-4a^3{b}^4\left(ii\right)\frac{2}{3}abby-\frac{1}{4}{a}^{2}b\left(iii\right)-5c{d}^{2}by-5c{d}^2\left(iv\right)4aand(6a+7)\left(v\right)-8xand(4-2x-x^2)\left(vi\right)2a^2-5a-4and-3a.\left(vii\right)x+4byx-5\left(viii\right)5a-1by7a-3\left(ix\right)12a+5bby7a-b\left(x\right)x^2+x+1by1-x\left(xi\right)2m^2-3m-1and4m^2-m-1\left(xii\right)a^2,aband{b}^2\left(xiii\right)abx,-3a^{2}xand7b^2{x}^3\left(xiv\right)-3bx,-5xyand-7b^3{y}^2\left(xv\right)(-\frac{3}{2}{x}^5{y}^3)and\left(\frac{4}{9}{a}^2{x}^{3}y\right)\left(xvi\right)(-\frac{2}{3}{a}^7{b}^2)and(-\frac{9}{4}a{b}^5)\left(xvii\right)(2a^3-3a^2{b}^2)and(-\frac{1}{2}a{b}^2)\left(xviii\right)(2x+\frac{1}{2}y)and(2x-\frac{1}{2}y)$

Q.

What is/are the factors of $a^2-b^2$?

1. $a+b$

2. $a-b$

3. ${a-b}^2$

4. ${a+b}^2$

Q.

Find the product $24x^2(1-2x)\text{and evaluate its value for}x=3.$

Q.

${11}^3+{12}^3+...{20}^3$

1. is divisible by $5$

2. is an odd integer divisible by $5$

3. is an even integer which is not divisible by $5$

4. is an odd integer which is not divisible by $5$

Q.

Simplify and find the value of the algebric expression if m=5 and n=10.

$\left(i\right){(m^2-n^{2}m)}^2+2m^3{n}^2$

$\left(ii\right){(7m-8n)}^2+{(7m+8n)}^2$

$\left(iii\right){(m^2-n^2)}^2$ [3 MARKS]

Q.

Find the following products and verify the result for x = -1, y = - 2:

$(3x-5y)(x+y)$

Q. Question 83 (ix)

Multiply the following:
(p + 6), (q - 7)

Q.

The adjacent sides of a rectangle are $x^2-4xy+7y^{2}and{x}^3-5x{y}^2$.Find its area.

Q.

Question 83 (xxi)

Multiply the following:

$(3x^2+4x-8),(2x^2-4x+3)$

Q.

Find each of the following products:

$(x^2-xy+y^2)\times (x+y)$

Q.

Question 1(iii)
Multiply the binomials:
(2.5l-0.5m) and ( 2.5l+0.5m)

Q.

Find each of the following products:

$(9x^2-x+15)\times (x^2-3)$

Q.

Tick $\left(✓\right)$ the correct answer in each of the following:
$(a+1)(a-1)(a^2+1)=?$
(a) $(a^4-2a^2-1)$
(b) $(a^4-a^2-1)$
(c) $(a^4-1)$
(d) $(a^4+1)$

Q. Question 83 (xv)

Multiply the following:
$(a^2-b^2),(a^2+b^2)$

Q.

Find the product $-3y(xy+y^2)\text{and find its value for}x=4andy=5.$

Q.

$\text{Find the product of}(7x-4y)\text{and}(3x-7y).$

1. $21x^2$ + $28y^2$ + $61xy$

2. $21x^2$ - $28y^2$ - $61xy$

3. $21x^2$ + $28y^2$ - $61xy$

4. $21x^2$ + $28y^2$ - $37xy$

Q.

Question 1(v)
Multiply the binomials:
$(2pq+3q^2)and(3pq-2q^2)$

Q. Question 83 (xvii)

Multiply the following:
(pq - 2r), (pq - 2r)