Question

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Answer 1

Answer:

1. 3xy² + y² + 2xy
2. (x² + y³)(a + 2)
3. x = 8
4. 6x² + 5xy - 6y² + 25x + 5y + 25

Step-by-step explanation:

Question 1:

Divide 15x²y² + 5xy² + 10x²y by 5x

$\sf{\longrightarrow} \: 15 {x}^{2} {y}^{2} + 5x {y}^{2} + 10 {x}^{2} y \div 5x$

$\sf{\longrightarrow} \: \dfrac{15 {x}^{2}{y}^{2}}{5x} + \dfrac{5x {y}^{2}}{5x} + \dfrac{10 {x}^{2} y}{5x}$

$\sf{\longrightarrow} \: 3x {y}^{2} + {y}^{2} + 2xy$

Answer : 3xy² + y² + 2xy

$\rule{300}{1.5}$

Question 2:

Factorize : x²a + y³a + 2x² + 2y³

$\sf{\longrightarrow} \: {x}^{2} a + {y}^{3} a + 2 {x}^{2} + 2 {y}^{3}$

$\sf{\longrightarrow} \:a( {x}^{2} + {y}^{3} ) + 2( {x}^{2} + {y}^{ 3})$

$\sf{\longrightarrow} \:( {x}^{2} + {y}^{3})(a + 2)$

Factors = (x² + y³)(a + 2)

$\rule{300}{1.5}$

Question 3:

If 3x - 4 = 20, then x = ??

$\sf{\longrightarrow} \:3x - 4 = 20$

$\sf{\longrightarrow} \:3x = 20 + 4$

$\sf{\longrightarrow} \:3x = 24$

$\sf{\longrightarrow} \:x = \dfrac{24}{3}$

$\sf{\longrightarrow} \:x = 8$

Value of x = 8

$\rule{300}{1.5}$

Question 4:

Expand : (2x + 3y + 5)(3x - 2y + 5)

$\sf{\longrightarrow} \:(2x + 3y + 5)(3x - 2y + 5)$

$\sf{\longrightarrow} \:2x(3x - 2y + 5) + 3y(3x - 2y + 5) + 5(3x - 2y + 5)$

$\sf{\longrightarrow} \: {6x}^{2} - 4xy + 10x + 9xy- {6y}^{2} + 15y + 15x - 10y+ 25$

$\sf{\longrightarrow} \: {6x}^{2} + 5xy- {6y}^{2} + 25x + 5y + 25$

Answer: 6x² + 5xy - 6y² + 25x + 5y + 25