Question

Pls answer these questions
Grade 7 algebraic expressions

Answer 1

Required Solutions :

Steps involved :

• Whenever we subtract algebraic expressions, we firstly collect the like terms in order.
• Then, we subtract it as usual substraction.

Subtract :

(I) $\sf{ -5{y}^{2} \: from \: {y}^{2} }$

We have to subtract $\sf{ -5{y}^{2} \: from \: {y}^{2} }$, ie

$\sf {\longrightarrow {y}^{2} - ( - 5{y}^{2} ) }$

As there is a minus (-) sign before the bracket, so (-) × (-) = (+) .

$\sf {\longrightarrow {y}^{2} + 5{y}^{2} }$

$\longrightarrow$ $\boxed{ \sf \red { 6{y}^{2} }}$

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$\sf{(ii) \: 6xy \: from \: - 12xy}$

$\sf {\longrightarrow - 12xy - 6xy }$

$\longrightarrow$ $\boxed{ \sf \red { 18 xy}}$

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$\sf {(iii) \: (a - b) \: from \: (a + b) }$

$\sf {\longrightarrow (a + b) - (a - b) }$

As there is a minus (-) sign before the bracket, so sign of the digits under the bracket will be changed when we'll remove the bracket.

$\sf {\longrightarrow a + b - a + b }$

Now, collect the like terms.

$\sf {\longrightarrow \cancel{ a - a}+ b + b }$

Performing addition.

$\longrightarrow$ $\boxed{ \sf \red { 2b}}$

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$\sf {(iv) \: a(b - 5) \: from \: b(5 - a) }$

$\sf {\longrightarrow b(5 - a) - a(b - 5)}$

Firstly, we will perform multiplication.

$\sf {\longrightarrow b(5) \times b( - a) - a(b) - a( - 5)}$

$\sf {\longrightarrow 5b - ab - ab + 5a}$

$\longrightarrow$ $\boxed{ \sf \red { 5b -2ab + 5a}}$

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$\sf { (v) \: {-m}^{2} + 5mn \: from \: 4{m}^{2} - 3mn + 8 }$

$\sf { \longrightarrow 4{m}^{2} - 3mn + 8 - ( -{m}^{2} + 5 mn )}$

$\sf { \longrightarrow 4{m}^{2} - 3mn + 8 + {m}^{2} - 5 mn }$

$\sf { \longrightarrow 4{m}^{2} + {m}^{2} - 3mn - 5 mn + 8}$

$\longrightarrow$ $\boxed{ \sf \red { 5{m}^{2} - 8mn + 8}}$

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$\sf { (vi) \: -{x}^{2} + 10x - 5 \: from \: 5x - 10 }$

$\sf { \longrightarrow 5x - 10 - ( -{x}^{2} + 10x - 5 ) }$

$\sf { \longrightarrow 5x - 10 + {x}^{2} - 10x + 5 }$

$\sf { \longrightarrow {x}^{2} + 5x - 10x- 10+ 5 }$

$\longrightarrow$ $\boxed{ \sf \red { {x}^{2} - 5x + 4}}$

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Answer 2

Subtract :-

(1) -5y² from y² = 6y²

(i) 6xy from -12xy = 18xy

ii) (a - b) from (a + b) = 2b

iv) a (b– 5) from b (5 – a) = 5a + 5b -2ab

v) -m2 + 5mn from 4m2 – 3mn + 8 = 5m² - 8mn + 8

vi) -x² + 10x - 5 from 5x - 10 = −7a² −7b² +10ab