Factorisation by Grouping

Q. Factorize each of the following expressions:

$a^4-16b^4$

Q.

Describe the relationship between using the Distributive Property to simplify an expression and to factor an expression. Give an example to justify your answer.

Q.

Factorize:

$y^3-3y^2+2y-6-xy+3x$

1. $-(3-y)(x-2-y^2)$

2. $(y-3)(y^2+2-x)$

3. $-(3-y)(y^2+2-x)$

4. $(3-y)(x-2-y^2)$

Q.

Factorise $a^2+7a+10$ + pa + 6p

1. (a+5) + (a+ 2+ p)

2. (a+5) + (a+ p)

3. (a+2) + (a+ 5+ p)

4. (a+7+ p) + (a+ p)

Q.

$\frac{16x^4}{49y^2}+\frac{49y^4}{16x^2}+2xy=(\frac{4x^2}{7y}+\frac{7y^2}{4x}{)}^2$

1. True

2. False

Q.

Factorise $b^2+c^2+2bc-a^2$

1. $(b^2+c)(c^2-a)$

2. $(b-c+a)(b+c-a)$

3. $(b+c+a)(b+c-a)$

4. $(bc+a)(bc-a)$

Q.

2ax + x can be factorised as ____________.

1. x( 2a+ 1)

2. a( 2x + 1)

3. 2ax

4. x + 1

Q.

$\text{Divide}{m}^2+7m-60\text{by}(m-5).$

1. 4(m - 6)

2. 2(m + 6)

3. (m + 12)

4. (m - 12)

Q. $x^2+7x+10$ can be factorized as

1. $(x+2)(x+5)$
2. $(x+3)(x+5)$
3. $(x+10)(x+1)$
4. $(x+5{)}^2$

Q. Number of terms in the expression, $7x^2+5xy$ is 2.

1. False
2. True

Q. $5xy+25y+3x+15$ is factorised as

1. $(5y+3)(x+5)$
2. $(y+3)(5x+25)$
3. $(y-3)(x-5)$

Q.

2x ( 3a + 4 ) is same as 6ax + 8x

1. True

2. False

Q. $x^2+6x+8$ can be factorized as $(x+2)(x+4)$

1. False
2. True

Q. Choose a common factor of $17abc,34a{b}^2,$ and $51a^{2}b$ from the given options.

1. $17ab$
2. $17a^2{b}^{2}c$
3. $17bc$
4. $17ac$

Q. Match the following algebraic expressions with their factorised form.

1. $x(3x+5)$
2. $(2x+6{)}^2$
3. $(x-4)(x+4)$
4. $5x(2x^3+6x^2+1)$

Q.

Factorize:

$y^3-3y^2+2y-6-xy+3x$