### Factorisation Class 8th Mathematics AP Board Solution

##### Question 1.Find the errors and correct the following mathematical sentences3(x – 9) = 3x – 9Answer:If LHS is3(x – 9)Then RHS would be⇒ 3(x – 9)= 3 × x – 3 × 9= 3x – 27The error is 27 instead of 9Hence 3(x – 9) = 3x – 27Question 2.Find the errors and correct the following mathematical sentencesx(3x + 2) = 3x2 + 2Answer:If LHS isx(3x + 2)Then RHS would be⇒ x(3x + 2)= 3 × x × x – 2 × x= 3x2 – 2xThe error is 2x instead of 2Hence x(3x + 2) = 3x2 + 2xQuestion 3.Find the errors and correct the following mathematical sentences2x + 3x = 5x2Answer:If LHS is2x + 3xThen RHS would be⇒ 2x + 3x= x(2 + 3)= 5xThe error is 5x instead of 5x2Hence 2x + 3x = 5xQuestion 4.Find the errors and correct the following mathematical sentences2x + x + 3x = 5xAnswer:If LHS is2x + x + 3x = 5xThen RHS would be⇒ 2x + x + 3x= x(2 + 1 + 3)= 6xThe error is 6x instead of 5xHence 2x + x + 3x = 6xQuestion 5.Find the errors and correct the following mathematical sentences4p + 3p + 2p + p – 9p = 0Answer:If LHS is4p + 3p + 2p + p – 9pThen RHS would be⇒ 4p + 3p + 2p + p – 9p= p(4 + 3 + 2 + 1–9)= p(10–9)= pThe error is p instead of 0Hence 4p + 3p + 2p + p–9p = pQuestion 6.Find the errors and correct the following mathematical sentences3x + 2y = 6xyAnswer:If RHS is6xyThen LHS would be⇒ 6xy= 2 × 3 × x × y= 3 × x × 2 × y= 3x × 2yThe error is sign of multiplication instead of sign of additionHence 3x × 2y = 6xyQuestion 7.Find the errors and correct the following mathematical sentences(3x)2 + 4x + 7 = 3x2 + 4x + 7Answer:If LHS is(3x)2 + 4x + 7Then RHS would be⇒ (3x)2 + 4x + 7= 32 × x2 + 4x + 7= 9x2 + 4x + 7The error is 9x2 instead of 3x2Hence (3x)2 + 4x + 7 = 9x2 + 4x + 7Question 8.Find the errors and correct the following mathematical sentences(2x)2 + 5x = 4x + 5x = 9xAnswer:If LHS is(2x)2 + 5xThen RHS would be⇒ (2x)2 + 5x= 22 × x2 + 5x= 4x2 + 5xThe error is 4x2 instead of 4xHence (2x)2 + 5x = 4x2 + 5xQuestion 9.Find the errors and correct the following mathematical sentences(2a + 3)2 = 2a2 + 6a + 9Answer:If LHS is(2a + 3)2Then RHS would be⇒ (2a + 3)2= (2a)2 + 32 + 2 × 2a × 3= 4a2 + 9 + 12a= 4a2 + 12a + 9The error is 4a2 instead of 2a2 and 12a instead of 6aHence = (2a + 3)2 = 4a2 + 9 + 12aQuestion 10.Find the errors and correct the following mathematical sentencesSubstitute x = – 3 in(a) x2 + 7x + 12 = (–3)2 + 7 (–3) + 12 = 9 + 4 + 12 = 25Answer:If LHS isx2 + 7x + 12Then RHS would be⇒ x2 + 7x + 12Putting x = (-3)= (–3)2 + 7 (–3) + 12= 9 + (-21) + 12= 21-21= 0The error is (-21) instead of 4 and end result 0 instead of 25Hence putting x = (-3) in x2 + 7x + 12 results to 0Question 11.Find the errors and correct the following mathematical sentencesSubstitute x = – 3 in(b) x2– 5x + 6 = (–3)2 –5 (–3) + 6 = 9 – 15 + 6 = 0Answer:If LHS isx2– 5x + 6Then RHS would be⇒ x2– 5x + 6Putting x = (-3)= (–3)2 –5 (–3) + 6= 9 + 15 + 6= 30The error is + 15 instead of (-15) and end results to 30 instead of 0Hence putting x = (-3) in x2– 5x + 6 results to 30Question 12.Find the errors and correct the following mathematical sentencesSubstitute x = – 3 in(c) x2 + 5x = (–3)2 + 5 (–3) + 6 = – 9 – 15 = –24Answer:If LHS isx2 + 5xThen RHS would be⇒ x2 + 5xPutting x = (-3)= (–3)2 + 5 (–3)= 9 + (-15)= -6The error is ( + 9) instead of (-9) and end results to (-6) instead of (-24)Hence putting x = (-3) in x2 + 5x results to (-6)Question 13.Find the errors and correct the following mathematical sentences(x – 4)2 = x2 – 16Answer:If LHS is(x – 4)2Then RHS would be⇒ (x – 4)2= (x)2 + 42 – 2 × x × 4= x2 + 16 – 8xThe error is x2 + 16 – 8x instead of x2 – 16Hence (x – 4)2 = x2 + 13 – 8xQuestion 14.Find the errors and correct the following mathematical sentences(x + 7)2 = x2 + 49Answer:If LHS is(x + 7)2Then RHS would be⇒ (x + 7)2= (x)2 + 72 + 2 × x × 7= x2 + 49 + 14The error is x2 + 14x + 49 instead of x2 + 49Hence (x + 7)2 = x2 + 14x + 49Question 15.Find the errors and correct the following mathematical sentences(3a + 4b) (a – b) = 3a2 – 4a2Answer:For getting in the equation(a2 – b2 ) = (a + b)(a-b)RHS would be3a2 – 4b2Then LHS would be⇒ 3a2 – 4b2= (3a – 4b)(3a + 4b)The error is (a – b) instead of (3a – 4b)3a2 – 4b2 instead of 3a2 – 4a2Hence 3a2 – 4b2 = (3a – 4b)(3a + 4b)Question 16.Find the errors and correct the following mathematical sentences(x + 4) (x + 2) = x2 + 8Answer:If LHS is(x + 4) (x + 2)Then RHS would be⇒ (x + 4) (x + 2)= x2 + 4 × x + 2 × x + 2 × 4= x2 + 4x + 2x + 8= x2 + 6x + 8The error is x2 + 6x + 8 instead of x2 + 8Hence (x + 4) (x + 2) = x2 + 6x + 8Question 17.Find the errors and correct the following mathematical sentences(x – 4) (x – 2) = x2 – 8Answer:If LHS is(x – 4) (x – 2)Then RHS would be⇒ (x – 4) (x – 2)= x2 – 4 × x – 2 × x + (-2) × (-4)= x2 – 4x – 2x + 8= x2 – 6x + 8The error is x2 – 6x + 8 instead of x2 – 8Hence (x – 4) (x – 2) = x2 – 6x + 8Question 18.Find the errors and correct the following mathematical sentences5x3 ÷ 5x3 = 0Answer:If LHS is5x3 ÷ 5x3Then RHS would be⇒ 5x3 ÷ 5x3= = 1The error is1 instead of 0Hence 5x3 ÷ 5x3 = 1Question 19.Find the errors and correct the following mathematical sentences2x3 + 1 ÷ 2x3 = 1Answer:If LHS is(2x3 + 1) ÷ 2x3Then RHS would be⇒ (2x3 + 1) ÷ 2x3= = = The error is instead of 1Hence (2x3 + 1) ÷ 2x3 = Question 20.Find the errors and correct the following mathematical sentences3x + 2 ÷ 3x = Answer:If LHS is(3x + 2) ÷ 3xThen RHS would be⇒ (3x + 2) ÷ 3x= = = The error is instead of Hence (3x + 2 )÷ 3x = Question 21.Find the errors and correct the following mathematical sentences3x + 5 ÷ 3 = 5Answer:If LHS isFor the complete and perfect divisionThere must be 3x instead of x(3x + 5)÷3xThen RHS would be⇒ (3x + 5)÷3x= = = The error is instead of 5 and 3x instead of xHence = (3x + 5)÷3x = Question 22.Find the errors and correct the following mathematical sentences = x + 1Answer:If LHS is Then RHS would be⇒ = x + = x + 1The error is x + 1 instead of x + 1Hence x + 1

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